Honestly, the pickings feel pretty slim when you look for that specific dynamic done well. There's a ton of fics where he just gets a cool dragon pet that acts like a large, scaly dog with fire breath, which kind of misses the point of a 'familiar' bond. The magical companion angle gets lost. I did read one ages ago, can't even remember the name, where a hatchling imprinted on him during the first task in 'Goblet of Fire'. It started strong with a neat psychic link, showing the dragon's ancient, alien thoughts, but then it just became a combat asset for the later tasks. Felt like a wasted opportunity.
What I'd love to see is a story that really leans into the ancient magic aspect. Dragons aren't just animals in that world; they're deeply magical creatures. A bond like that should change Harry, maybe give him insights into older, wilder magic that wanders and wizards have forgotten. It could create conflict with the very structured, 'civilized' magical society he's part of. Instead of the dragon solving his problems, it could create new ones—how do you hide a creature like that? How does it affect his relationships? Most fics I've stumbled across use the dragon as a power-up, not as a catalyst for a different kind of character exploration. Makes the whole concept feel undercooked.