one that doesn't have to follow canon, i mean he can be involved with hp but does not center around him so much, i mean come on, some authors underestimate butterfly effect too much, u being there can affect so much already
You could check on this page for Harry Potter story but if you specifically want reincarnated it's a little bit more difficult. https://www.fanfiction.net/book/Harry-Potter/?&srt=4&lan=1&r=10 There is Harry Potter and the Game, not reincarnated but a gamer HP is always a good story even thought it's on hiatus. Harry Potter and the Methods of Rationality is a good change of pace. It's not a reincarnated but more like a different Harry Potter. Harry Potter and the Natural 20. More like someone got transported over there but with D&D system of magic. Harry Potter and the Critical Game, here Harry is reincarnated. Harry Potter and the Nightmares of Futures Past. Still not reincarnated but Harry is going back in time. Heroes Assemble! Is a good Crossover between HP and Marvel Avengers.
On webnovel, there is Harry Potter and the Mystical Journey. Tangled journey in Harry Potter. Those two are on hiatus or discontinued but it can make you busy a little bit. On royalroad there is, Taking on the magical world, I don't really follow it anymore but it suit what you want. And the best of all the Harry Potter stories that I read is : Magical Adventure, really great story, that is always being updated every Monday. An inexplicable reincarnation into the magical world of Harry Potter!! An avid fan of the series is born into this magical world with quite detailed knowledge about it. With his fore knowledge, he has the ability to influence the timeline or characters in many ways. Let us see how the story unfolds now …. after this new character has entered it.
The OCs/SIs of Harry Potter A Collection of Self Insert Fics Most SI/OC fics are reincarnated ones so here are some collection of it in HP World. Enjoy.