One theory is that Remus Lupin could be Harry's real father. Lupin was a close friend of James and Lily. In fanfiction, writers might explore the idea that there was something more between Lupin and Lily. Maybe Lupin's werewolf nature was somehow involved in a magical way that led to Harry's conception, creating a whole new backstory for Harry that is very different from the original story.
One interesting theory is that Harry's real father was an ancient and powerful wizard who time - traveled to be with Lily. This wizard was on a mission to change the future of the wizarding world and saw Lily as the key. So he had a relationship with her, resulting in Harry. It's a wild concept that plays with the idea of time magic in the Potter universe.
In some fanfictions, it could be Sirius Black. Some fans like to imagine that Sirius had a deeper connection to James Potter's family than just being best friends. They might create a scenario where there was some sort of magic or prophecy involved that made Sirius more than just Harry's godfather, but his actual father in this alternate story line.
Well, a conspiracy in Harry Potter fanfic could be about Dumbledore. Some fanfictions claim he knew a lot more about Voldemort's Horcruxes long before he let on. Maybe he was waiting for the right moment to act for some secret reason, like he was testing Harry in a more extreme way than we thought. It makes for really interesting stories as it changes the way we view Dumbledore's actions throughout the series.
In some fanfictions, Sirius Black is sometimes portrayed as Harry Potter's real father. This idea might stem from Sirius's deep connection and loyalty to Harry, as well as his role as a father - like figure in Harry's life.
One theory could be that Naruto has a hidden bloodline trait related to chakra regeneration that is only explored in fanfiction. Maybe it was dormant before and gets activated through some extreme situation in the story.
One possible scenario in a fanfiction of Harry Potter's father and a Murkrow could be that the Murkrow is actually a transformed Animagus. James Potter might initially be suspicious of it but then realize it's an ally in some sort of secret mission against the Dark Arts. Since James was part of the Marauders, he was always into adventures, and this could be one such adventure involving a strange creature like the Murkrow.
Perhaps Harry's different father could be a Muggle - born wizard who was experimented on by dark wizards. This would give Harry a connection to a darker side of magic that he has to come to terms with. He might have inherited some unique powers or curses from his father. Or his father could be a wizard who was in hiding from Voldemort for reasons other than what we know in the original story. This could change the dynamic of the prophecy and Harry's role in the fight against Voldemort.
Another theory could be that her real parents were wrongly accused of a crime in the wizarding world and had to give her up. In the fanfic, Hermione might find out about this and try to clear their names. It could be a long and difficult journey filled with mystery and danger.
Another possibility could be Draco Malfoy. Think about it. In some fanfictions, they might rewrite the relationships completely. Draco has his own complex character arc, and perhaps in this 'harry potter is not the father' scenario, he ends up being the father due to some unforeseen circumstances, like a misfired spell that alters the course of events related to parentage.
One idea could be that Harry's new father is a powerful wizard from a different magical society. This could introduce new types of magic and cultures into the story.