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.
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.
Obviously, Percy is one of the main characters. But there could be others depending on the specific plot of the fanfiction. Maybe there are some characters from Percy's past that play important roles.
Perhaps Percy will discover secrets about his family or his powers that were previously unknown. Since he's in the past, there could be ancient magic or knowledge that he stumbles upon. This newfound knowledge could give him an edge when he returns to his own time, if he ever does. He might also face challenges like trying to blend in with the people of the past, as his modern ways could make him stand out and cause suspicion.
The plot might involve Percy going back in time and getting involved in a love story that was lost to history. He could fall in love with someone from the past and then have to make a difficult choice when it comes time to return to his own time. It could also be that he has to use his modern knowledge to solve problems in the past that no one else could figure out, which then changes the course of history in small but significant ways.
One common theme is self - discovery. When Percy is sent back in time, he often has to re - evaluate who he is without all the experiences he had in his original timeline. Another theme is the butterfly effect. His actions in the past can have huge consequences for the future. For example, a small decision he makes might change the entire course of a battle.
One character could be a time - keeper or a wizard who has the power to send Percy back in time. This character could be an old and wise figure, full of knowledge about the past and the ways of time travel. Another could be a historical figure that Percy meets in the past. For example, a famous warrior or a philosopher who becomes Percy's ally or mentor.
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.
In such a fanfiction, Percy might use his knowledge of the future to change some key events in the past. For example, he could prevent some of the earlier disasters or conflicts in the Percy Jackson universe. Maybe he'd try to stop the first encounter with a certain monster in a different way to avoid the chaos it caused.