I've noticed a few distinct patterns, mostly adaptations of the 'Harry raised by different people' trope, but the Slytherin setting shifts the focus. Instead of the usual political maneuvering, the better ones use the house's pragmatic, self-preservation ethos as a lens for Harry's character deconstruction. It’s rarely about him being evil. More often, it starts with the hat’s logic in the first book—ambition, resourcefulness, a thirst to prove himself—and runs with that seed. His journey becomes about unlearning the black-and-white morality he might have absorbed from the Dursleys and wizarding legend, navigating a world where allies and enemies aren't defined by house colors.
A central conflict becomes his relationship with his own legacy. In Slytherin, he's surrounded by whispers about his parents, Voldemort, and pure-blood politics. His journey often involves sifting through biased history to form his own identity, separate from both Dumbledore's 'symbol of hope' and the Death Eaters' 'pure-blood savior' narratives. This leads to a kind of intellectual isolation, even if he makes friends like Daphne Greengrass or Theo Nott. The climax isn't always a big battle; sometimes it's a quiet, ruthless political play that outmaneuvers both Dumbledore and Voldemort, cementing his own path.