A possible plot is that Harry, after being left by his parents, is raised by a wizard who lives in seclusion. This wizard has a very different view of magic compared to the mainstream wizarding world. Harry learns from him and as he gets older, he decides to go out into the world to seek revenge on those who he believes are responsible for his parents leaving him. Along the way, he meets new friends and foes and has to make some tough decisions about his path in life.
Perhaps Harry is disowned because his parents believe he has been corrupted by dark magic. So he has to prove his innocence and find a way to reverse their decision. Along the way, he meets a mentor who helps him master his magic in a new and unique way, different from what he would have learned from his parents.
One plot idea could be that Harry has to face the Boggart - his parents - in a more public setting than expected, like during a school-wide anti - dark arts demonstration. This could add an extra layer of pressure as he tries to keep his emotions in check. Another idea is that the Boggart - parents might start interacting with other students' Boggarts, creating a chaotic and emotional mess in the classroom. Maybe the Boggart - parents could also show signs of the dark magic that killed them, which would terrify Harry even more as he realizes how close he is to that danger.
In a fanfiction about Harry Potter and his parents, a great plot could be that Harry discovers a hidden diary of his mother. Through reading it, he gets to know her deepest thoughts, her fears, and her hopes. He also learns about the early days of the Order of the Phoenix through her eyes. This discovery could change his perspective on his own life and his place in the wizarding world. He might then be inspired to follow in his parents' footsteps more closely, perhaps by joining an organization that his parents were once part of.
One idea could be that James and Lily Potter go into hiding with Harry instead of being killed. They could use powerful magic to disguise themselves and Harry, and then raise him in a secret location, teaching him magic from a very young age. This would change Harry's whole personality as he would grow up with the love and guidance of his parents.
Well, perhaps they have a child who is really interested in Muggle studies, much to the amusement of Harry who has some Muggle - like tendencies. And they struggle a bit with how to balance their child's interest in Muggle things with the wizarding world they live in. Also, there could be a plot where the family has to deal with some old enemies of Harry's who are seeking revenge, but this time they have to protect not just themselves but also their child. It could show how they use their combined skills and knowledge to keep their family safe.
Well, perhaps Harry uses a time - turner that has been magically enhanced to travel far enough back. He could disguise himself and befriend his parents, subtly guiding them to safety. Or he could change the circumstances of their meeting, for example, if he makes sure that they meet in a more secure place. Also, he could try to influence the actions of the Marauders so that they are more vigilant in protecting his parents.
A third plotline might be that Harry is abandoned in a magical but hidden place. There, he is raised by magical creatures, say, a group of centaurs. They teach him their own brand of magic and wisdom. When he finally enters the wizarding world proper, he has a very different perspective on magic compared to the other students, which causes both admiration and some envy among his peers.
A plotline could be that Harry, after being dumped by his parents, has a very different personality. He's more withdrawn and distrustful. Sirius has to work hard to break through those walls. They could travel to different magical places to find a way to reverse what Harry's parents did or to find out the real reason behind it. Along the way, they meet other characters who either help or hinder their journey, and this all shapes their relationship and Harry's growth as a person.
One possible plotline could be Harry growing up in an orphanage where he discovers some latent magic powers on his own before getting his Hogwarts letter. He might face more difficulties and prejudices from the muggles around him, which could make his entry into the wizarding world even more of a relief.
One plot idea could be that Harry is blindfolded and without his glasses during a dangerous game at Hogwarts. His friends have to guide him through a series of magical obstacles using only non - visual cues. Another could be that a spell has made him blindfolded and lost his glasses, and he discovers a new magical sense within himself to navigate the wizarding world. Maybe in a situation where he's kidnapped by dark wizards, they take his glasses and blindfold him, but he manages to escape using his other skills and the help of some unexpected magical creatures.