I'm not sure there are a huge number of these very specific fanfics, but 'The Bottom - Bound Time Travel of Harry Potter' might be worth checking out. It delves into how Harry's unexpected time journey because of his bottom changes his perception of magic and his relationships with other characters. It's a wild ride that plays with the time - travel trope in a very unique way.
One popular fanfic in this vein is 'Time's Twist for Harry's Bottom'. It explores the unique concept of Harry being sent back in time due to a magical mishap involving his bottom (in a rather comical way). Another one could be 'Back in Time, Bottom First' which has an interesting plot where Harry has to deal with the changes in the past while his bottom - being the source of the time - travel has some strange side - effects.
One common theme is self - discovery. Since Harry is sent back in time, he gets a chance to see his past self and the world in a new light, which often leads to him learning more about his true nature. For example, in some fanfics, he realizes his hidden strengths or weaknesses. Another theme is the alteration of the timeline. His presence in the past can change small or large aspects of the future he came from, and the fanfics usually explore the consequences of these changes.
One great 'Percy sent back in time' fanfic is 'Back to the Beginning'. It shows Percy having to deal with all the early threats in a new way. Another is 'Time - Twisted Percy' which has an interesting take on how his knowledge of the future changes things. There's also 'Percy's Time - Travel Adventure' where he forms unexpected alliances in the past.
Well, Percy is obviously one of the main characters since it's about him getting sent back in time. There might also be his friends like Annabeth. In the past, he could meet characters who are important in the history of his world, like the ancient gods or heroes. They would play significant roles in his journey back in time as he might need their help or they could be obstacles in his way.
Well, perhaps a major plot twist is when Percy goes back in time and realizes that the events he thought were accidents in his own time were actually carefully orchestrated by a character from the past. This would add a whole new layer of mystery and conspiracy. Also, he might find that a prophecy he was trying to prevent in his time was actually meant to happen in the past for a greater good, which would be a huge turn for his mission.
Harry himself is obviously a very popular character in these fanfictions as he is the one being sent back in time. But also, characters like Sirius Black are often popular. Fans like to explore how Sirius would react to Harry being in the past, and how their relationship could develop differently.
One interesting plot could be Harry going back in time and preventing certain tragedies from happening in the wizarding world, like stopping Voldemort's rise before it really began. Another could be him changing the relationships between characters, for example, making Snape and James Potter become friends early on.
Definitely Harry himself. Since he is the one being sent back in time, he is central to the story. His actions and decisions in the past are what drive the plot forward.
There could also be a powerful magical creature that has been corrupted by dark magic. This creature might be feared by all in the past, and when Harry arrives, it sees him as a new target or a potential source of power. Harry has to figure out how to defeat it using his own skills and the limited resources available in the past.
One interesting plot twist could be that Harry goes back in time and accidentally changes the sorting of some of the characters. For example, Draco Malfoy could end up in Gryffindor instead of Slytherin, which would completely change their relationship and how events unfold in the wizarding world.
Another amazing one is 'Back to the Beginning'. This fanfic takes the idea of time - travel and uses it to explore the early days of Hogwarts and the relationships between the founders. It's filled with a lot of mystery and intrigue as the main character tries to figure out how to use their time - traveling ability to make things right in the past without completely disrupting the present.