Percy could time travel to a world where his parents are aliens. This would be a really out - there concept. His powers might be enhanced or changed by his new alien heritage. He'd have to deal with a whole new set of cultural norms and abilities. His quest would be not only to understand his new parents but also to find a way back to his own world while still being true to his new self.
Imagine Percy traveling back to a time when his parents were heroes in a different way. His mother could be a great warrior and his father a wise leader. Percy would have to learn from their example in a different way than he did with Poseidon. He might have to unlearn some of his old ways and adapt to a more archaic style of heroism. It would be a story of growth and adaptation.
One idea could be that Percy travels back in time and ends up with a set of powerful wizard parents in a world where magic and demigod powers collide. He might struggle to adapt to a new family dynamic while still having his old skills and memories. For example, his new parents could be strict about magic use, which is very different from his demigod upbringing.
Finn's parents in Adventure Time fanfiction can have really interesting backstories. Maybe his mother was part of an ancient race that was hunted, and she hid Finn to protect him from the same fate. His father might have been a member of the human tribe that was scattered across the Land of Ooo. Fanfiction allows for different interpretations of how Finn came to be alone as a baby. It can be really exciting to read different authors' ideas on this.
Hermione's cautious and studious nature would likely make her approach the time - travel adventure with a lot of research and planning. She'd want to make sure they don't disrupt the timeline too much. Sirius, on the other hand, is more impulsive and adventurous. He might be eager to jump into action and explore the new time period without thinking of the consequences. This contrast could lead to some conflicts between them during the adventure. For example, Sirius might want to immediately confront his younger self, while Hermione would try to stop him.
Percy is impulsive. So in time travel, he might rush into situations without fully thinking about the consequences. For example, he could see a monster from Greek mythology in a different time period and immediately attack it, not realizing that this action could change the future. Artemis, on the other hand, is more calculating. She would likely try to analyze the situation first, like figuring out how the time period they are in affects the monster's behavior and power.
I really like 'The Time Traveling Lich'. In this fanfiction, the Lich uses time travel to try and rewrite history in his favor. It's full of action and has some really interesting twists on the characters' relationships. It shows how time travel could completely change the power dynamics in the Adventure Time universe.
In many such fanfictions, Naruto and Hinata might be sent back in time through some magical or jutsu - related means. Once they meet their parents, it could be a very emotional moment. Naruto might see his father Minato and mother Kushina, and Hinata could meet her father Hiashi. They could learn a lot about their families' pasts and perhaps even change some things for the better in the timeline.
In Adventure Time Finn Parents Fanfiction, a frequently seen concept is that Finn's mother was a princess from a forgotten kingdom. She might have fallen in love with Finn's father, a commoner. But due to political unrest or some dark magic, they had to separate and leave Finn. Also, the idea that Finn's parents were time - travelers is quite popular. They could have been sent back in time and got stuck, leaving Finn behind as they tried to fix the time - rifts they created.
Gohan could also time - travel to a point in Saiyan history. He might witness the destruction of Planet Vegeta and try to save some of the Saiyans. This would completely change the course of the Saiyan race and his own story. He'd have to deal with the cultural differences and the power - hungry nature of some of the Saiyans he saves.
Archive of Our Own (AO3) is another great place. It has a well - organized tagging system. So when you search for Adventure Time fanfiction with time travel, you can easily filter through different ratings, pairings, and other aspects to find exactly what you're looking for.
A mystery - genre Ino time travel fanfiction could be interesting. She could travel to a time where there are unsolved ninja mysteries. Her ability to read minds might help her solve these mysteries, but she also has to deal with the cultural and technological differences of that time.