A couple years ago, my friend ran The House of Lament, the starter adventure in Van Richten's Guide to Ravenloft. As a joke, initially, the character I came up with for it was Alexander von Zarovich, a dhampir rogue who was the son of infamous Darklord Strahd von Zarovich. His backstory was that he had been initially born as a means for Strahd to escape the Domains of Dread (back during Strahd's collaborations with Azalin) by essentially creating a suitable vessel to transfer his soul into while leaving his soulless body behind to remain trapped as Darklord. The experiment failed, and so Strahd transformed his son into an assassin, sent to terrorize his enemies. When Alexander accidentally killed the current incarnation of Tatyana, Strahd cast him out, banishing him to the Mists. Finding himself in Lamordia, he lived as an orphan but was taken in by a kindly adult who helped rehabilitate and de-program him, allowing him to grow into a (relatively) well-adjusted adult.
While the idea of a dhampir son of Strahd was the kind of one-shot joke character, I actually realized the concept had legs (hence the extensive backstory). I haven't had an opportunity to play this character in a larger campaign, but I could see myself doing so.
Naturally, there's some precedent from the Castlevania series, with the character of Alucard, aka Adrian Tepes, the son of Dracula and his human wife Lisa. As a Dhampir, Alucard heroically opposes his monstrous father while also being a bit of an edgelord himself.
Initially, my idea for Xander would be as a Rogue - that's how I played him in the House of Lament - but while I like that conceptually, I think A: a little frustration with the Rogue as a class and B: a desire for a more effective melee fighter has led me to consider an alternative.
Initially I thought maybe a fighter, probably a Dexterity-based one using a Rapier or perhaps dual-wielding. And then it struck me:
Bladesinger.
While I tend to prefer my Battlemages heavily armored, the Bladesinger does satisfy that definition of being a character who can use both spells and weapons (I know that "Battlemage" means other things to different people - to me I think it's kind of the less IP-specific "Gish" idea, which is best embodied in D&D with the Eldritch Knight Fighter subclass).
Not only is the Bladesinger a cool and powerful subclass, but it also, I think, fits well with the aesthetic of a vampiric warrior - vampires are rarely seen wearing armor, for example. They also tend to have magic powers, and we're going to be looking at a lot of the spells I'd choose to fit in with these themes (which also happen to go together for the most part).
I've got a build here that goes to level 10.
The 5.5 Bladesinger, from Heroes of Faerun, makes them a little less dependent on having high Dexterity, because you can now use Intelligence to attack while in your Bladesong. I do think you'll still want at least decent Dex, as it still raises your AC, initiative bonus, and of course helps with Dex saves. Potentially you could go with 15s in Int, Dex, and Con, though I tend to prefer starting with a 17 in my top stat at level 1 in 5.5 so that I can put it to 18 at level 4 with a General Feat.
Naturally, we'll be grabbing War Caster at level 4, which A: is basically what every spellcaster should take at level 4, but B: also really good given that we'll be mixing it up in melee and being able to Booming Blade as an opportunity attack.
Given the desire to have some feats in tier 3 to boost Dex and/or Con, I'm going to actually say we just push Int to 20 at level 8, rather than taking another Int-based General feat. Shadow Touched would certainly be thematic here, and there are some other Int-based feats to consider, but I have an OCD thing about capping stats.
For weapon choice, there are lots of options, because you're basically going to get a d8 weapon at best - even if you fight with a longsword, you can't use its versatile property without ending Bladesong, and given that you don't get weapon masteries, it's really just a choice of damage types. Thematically, I really feel like we've got to go with the Rapier, which just feels like the elegant vampiric weapon to pick. I could see a Whip also working, which sacrifices 2 damage on average for extra reach. That reach could be very helpful as a (somewhat) squishy Wizard, but I'm going to say let's risk it.
Now, spells:
For cantrips, the must-haves are Booming Blade and Green-Flame Blade. The former is particularly good as an opportunity attack with War Caster (unless your DM is an insane stickler and says that the spell targets the weapon, rather than the target of the attack). We can start off with True Strike if we're beginning at level 1 in order to be able to attack with a weapon before we get our subclass, but we might want to just stick to the back until then. We might consider having a ranged cantrip (Mind Sliver feels on-theme and is also good) but these are going to be our bread-and-butter. Blade Ward is also a decent choice, as once we get to level 6 and get our special Extra Attack, we can pop this up to effectively increase our AC by 1d4 on each hit (though it does eat up our concentration, so this might be better if we're in a big dungeon crawl with a lot of smaller fights where we don't want to blow a high-level spell slot on something).
First level, we want to grab Shield and Mage Armor. We cannot wear armor in the Bladesong (a change from the old version) so this will be our best option for armor unless we can get something like a Robe of the Archmagi or something far later on. Remember that Bladesong doesn't change the math of how we determine our armor - it just adds our Int modifier to AC, so if we have a +2 to Dex, Mage Armor, and +3 to Int at level 3, that's a healthy 18 AC, which will be better than even heavy-armor wearers unless they have a shield or somehow snagged plate this early. I'd also take Absorb Elements, another staple. Staples like Find Familiar (feels like it should be a bat) and Identify/Detect Magic are also good - we will still be a Wizard, and people will rely on us for stuff like that. I also like Jump here, which helps with our mobility as a melee wizard and again, feels very much like a vampire thing to do.
Second level, another spell I'd take on any character, Misty Step feels particularly good for our vampire theme (doesn't Alucard have an ability in Symphony of the Night where he turns into mist to go through barred barriers?) This is such a staple spell that I have zero hesitation putting it in there. It'll also potentially help us get to foes faster. Invisibility is another good utility spell that, again, lends itself to our spooky vibes.
Third level, there are a few standard choices (I'll never not take Fireball on a Wizard,) and Fear is a really good and again, thematic choice for our big Crowd Control spell. However, we now have an interesting question: Do we take Spirit Shroud? I made a post last fall comparing this spell to Conjure Minor Elementals. The short story: Spirit Shroud is more convenient, but doesn't scale as well. Each adds damage to attacks you make if the target is within a relatively close emanation, which is really powerful when you can make lots of attacks (it pairs well with Scorching Ray,) and given that our Bladesinger can regularly make two attacks per turn starting at level 6, we can often benefit from this. Spirit Shroud is less damage, but I do think it's way more thematically on-point than CME. It also only requires a bonus action to cast it, so we can start attacking on the same turn. That said, we also need our bonus action to activate Bladesong, so we probably won't be casting it until turn 2 in combat. Now, that's not really a downside given that if we have CME, we'll probably be activating Bladesong and then casting that on turn 1 and not attacking until turn 2 anyway - with Spirit Shroud we can at least attack in a non-augmented way on turn 1. So, it really depends on A: how long your combat lasts and B: how much you can upcast your spells. While I took CME on my D&D Beyond build of the character, I might actually argue that you should go Spirit Shroud if for no other reason than it feels way more on-theme. For other 3rd level spells, I like Summon Undead - all the Summon spells are pretty good, and both add a body to the field and do pretty decent damage (Summon Undead also has great utility, as the Ghost can automatically frighten anyone they hit, and the Putrid spirit requires some set-up and for monsters that aren't immune to being poisoned, but can paralyze things).
Fourth level, Polymorph is a key one - being able to turn into a Wolf or a Bat (talk with your DM about re-skinning higher-CR beasts so you can stay on-theme) is another big vampire trope. Conjure Minor Elementals is less thematic but still great for any Wizard who makes attack rolls. Greater Invisibility can be a really strong spell for both attack and defense if you can spare the concentration.
Rounding things out at 5th level, I think we've got to take Steel Wind Strike, which is a weird sort of pseudo-AOE spell that works very well with the idea of a weapon-wielding Wizard. It plays well with Spirit Shroud/CME, and while it's limited to 5 targets, how often do you get 5 targets in a Fireball? I also grabbed Danse Macabre, which is mostly just fun but I also think not all that bad - considering that Skeletons in 5.5 now have a base attack bonus of +5, if your Int is maxed out, they'll have a +10 to hit and deal 1d6+8 damage on each attack. With five skeletons shooting bows, that's 5d6+40 damage. Against an AC of 18, that's 38.25 average damage per turn. It is dependent on how many skeletons you have access to.
In terms of gameplay, there are some arguments that even a Bladesinger should mostly play like a standard Wizard most of the time, holding back from the fray. But to that, I say: why don't you want to have fun? Truly, by level 10, we're going to be pretty resilient - with +5 to Int, Mage Armor, and still just +2 to Dex, we're going to have an AC of 20 during Bladesong that can then be bumped to 25 if we get hit thanks to the Shield spell. If we get Bracers of Defense, raise those by 2. We might even consider starting with a +3 in Dex, though I generally think a Wizard should favor Con more than Dex, as not all damage requires them to hit you with an attack, and you still only have a d6 hit die. At level 10, we can expend spell slots as a reaction to reduce incoming damage by 5 times the spell's level. I think judicious use of that feature is an important challenge for the Wizard using it - reducing the damage of a dragon's breath, for example, could make it possible for you to maintain concentration on a spell.
One of the fun things about playing this as a Dhampir is that you could, in theory, have a fight along walls and ceilings, which does feel like a fun idea for a rapier-wielding warrior. Being based in Con, and with very few ways to increase the damage, I don't think you'll be using the bite attack all that much, but that's kind of true for all dhampirs.
We will be getting an update to the Dhampir in Ravenloft: Horrors Within, though I don't know how much is likely to change (I suspect not a ton, though they seem to be presenting the Gothic Lineages as more just full-on species in their own right, so we might have some changes to Ancestral Legacy).
At level 10, we get 5 Bladesongs per long rest, so we can probably expect to have it active every fight unless we're in serious dungeon-crawl mode. If we do run out, I think we just hurl spells from afar or focus on buffing allies.
When we want to bring our A-game, we spend the first turn activating Bladesong and then going in for the attack (if we're close enough - we should have a 45-foot movement speed) with a Booming Blade on single targets or Green-Flame Blade if we can hit a secondary target. On turn two, we'll want to activate Spirit Shroud at 5th level (we always want to cast it at odd levels, given how it scales) and then attack again, now dealing 2d8 extra damage (our choice of radiant, necrotic, or cold - radiant's probably the most reliable, but thematically we might go necrotic more often than not) per hit. Again, if we are using CME instead (also at 5th level, this now adding 3d8 to our attacks - I feel like Fire damage would be the thematically appropriate one, though Cold also works. Just pick the right one for the monsters you're fighting), we'll spend our first turn setting up, getting Bladesong and CME running, and then turn two we'll use our action to either attack or if we have a target-rich environment, we can do Steel Wind Strike, hitting each foe for both the spell's 6d10 and the bonus d8s. Note that this will blow both our 5th level slots, so we should only burn both of these spells if we want to burn a lot of gas.
If we want to be a little more conservative, casting either Spirit Shroud or CME at base level is an option. Greater Invisibility is also a decent choice (assuming your foes don't have Blindsight/Truesight).
Again, we are a Wizard, so we have tons of alternatives given the situation. Fear, for example, can seriously thin the ranks if we're facing a massive horde of foes.
When facing a hard-hitting foe, we can run in, attack, and then Misty Step to avoid their strikes if we're not sure Shield will be enough to keep us safe. Also, if you want to play it extra-safe and conservative, consider Blade Ward as your concentration spell, which you can cast on turn 1 after Spirit Shrouding with your Extra Attack. This feels ideal for minor fights in a dungeon room - I'm thinking specifically the vineyard in Curse of Strahd that is overrun with Blights - each fight is trivial, but there are so many little fights there that they can chip away at your HP and resources.
Anyway, I think this could be a very fun archetype - while the Bladesinger can work in any campaign, I do think that it's a strong choice for a lithe, elegant dhampir warrior in a very gothic campaign.