A really cool MHA Harry Potter crossover fanfiction is 'Heroes at Hogwarts'. In this story, the unique powers of the MHA characters interact in fascinating ways with the magic of Harry Potter. For example, Deku's One for All quirk has some unexpected interactions with spells. It's a must - read for fans of both series.
Another option is Reddit. There are subreddits dedicated to fanfiction, like r/FanFiction. You can post a request for MHA Harry Potter fanfiction there, and the community might be able to recommend some great reads. Also, sometimes people share their own works on these subreddits.
The magic system could be incorporated by having Hogwarts - like schools in the MHA universe. Teachers could teach spells and potions, and students would develop their magical abilities as they do their quirks. Magic could also be used in combat situations in the MHA world. For instance, a character could use a levitation spell to gain an advantage in a fight against a villain. This would add a new layer of strategy to battles in the MHA world.
A cool plot might be that the Hogwarts students attend U.A. High School. Hermione would surely excel in academic subjects there, while Ron could struggle a bit more. And Harry could use his experience with fighting dark magic to help in hero training. They could also introduce magic - based quirks to the MHA world, which would change the dynamic of how heroics are done.
One interesting crossover could be the magic system of Harry Potter being introduced to the MHA world. For example, a character from MHA might discover they have magical abilities like a Hogwarts student. Another could be the heroes from MHA having to face off against dark wizards from the Harry Potter universe. It would be a really cool mix of the two different power dynamics.
One possible plotline could be that Charlus Potter imparts some long - forgotten family magic or knowledge to Harry. This knowledge could help Harry in his fight against Voldemort in a different way than in the original books. Another plotline might be that Charlus Potter is brought back from the past through some time - travel mishap, and he has to adapt to the modern wizarding world while also guiding Harry. Or, it could be that they meet in a dream - like realm, and Charlus gives Harry cryptic messages about his future and the Potter family's true destiny.
A really cool fanfiction idea is that James Potter meets Harry Potter in an alternate universe. In this universe, James never died and he gets to see Harry as a normal, happy kid without the burden of being 'The Boy Who Lived'. They might go on adventures together in Hogwarts that are more about exploration and fun rather than fighting dark forces. Another interesting one could be where James Potter appears as a ghost to Harry Potter. He gives Harry advice on how to deal with his love life, something that James was quite good at during his own Hogwarts days.
I think Harry Potter himself would be very powerful in this crossover. He has the experience of fighting dark wizards and his magic skills. If he was in the MHA world, he could use his magic to enhance his physical abilities like the characters with quirks. His ability to resist the Imperius Curse and his knowledge of defensive magic would give him an edge over many MHA villains.
Perhaps his grandparents were great adventurers in their time. They could have traveled to far - off magical lands and encountered strange and wonderful things. Their experiences could be passed on to Harry, inspiring him to explore more of the wizarding world and its secrets. They might also have been involved in some great battles in the past, and their war stories could give Harry valuable lessons for his own fight against Voldemort.
It's hard to say. Harry has magic, which is a very powerful force within the wizarding world. But the Doctor has his time - traveling TARDIS and a vast knowledge of the universe. If it's a battle of raw power in a magical sense, Harry might have the upper hand. But if it's about outsmarting an enemy or finding solutions across different dimensions, the Doctor would be very strong.