He could meet his parents when they were young. Maybe he'd get to see his mother before she met his father and understand more about her life back then.
He could also learn new skills or knowledge from the past. There might be ancient powers or secrets that were lost over time. By traveling back, Percy could discover these and bring them back to his own time to use against his enemies. Also, he could interact with old heroes and learn from their experiences, which would make him an even better hero in his own time.
He could potentially change some events in the past that had a big impact on his present life. Say, he could prevent some of the early attacks by monsters that made his life so difficult growing up. This would completely alter the course of his life and the lives of those around him. It's a really cool concept to think about how one small change in the past could have a huge ripple effect in the future.
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.
In a fanfiction where Percy Jackson travels to the past, he might try to prevent some of the tragedies that occurred in the past. For example, he could attempt to stop the first Titan War from starting. He might use his skills and knowledge from the present to change the course of history, but this could also have unforeseen consequences, like disrupting the timeline and creating alternate universes.
Well, Percy could end up changing the entire course of history in the 'Percy is thrown back in time' fanfiction. He might accidentally stop some important relationships from forming or start new ones that were never meant to be. Also, he could have a chance to see his loved ones who are no longer alive in his original time, which would be an emotional rollercoaster for him.
Well, he might change some crucial events. For example, he could prevent some villains from ever rising to power. Maybe he'd stop Frieza from destroying Planet Vegeta earlier, which would change the whole Saiyan history and his own life. He could also teach his past self some new techniques, making the Saiyans even stronger in that timeline.
His unexpected ally could be a minor god from the past. Maybe a god that was forgotten in his own time but still has some power in the past time period Percy travels to. This god could help Percy because they see an opportunity to regain some status through Percy's actions in the present time. Another possibility is an enemy from his own time who has different motives in the past and ends up working with Percy.
Percy could change the past and accidentally create a new future. For example, if he stops Chronos from a certain event, it might have unforeseen consequences for the demigod world he knows. He might return to his own time to find that his friends are different or that Camp Half - Blood has changed drastically.
His relationship with his father Poseidon would be different. He might see a side of Poseidon that he never knew before, like when Poseidon was younger and less experienced. This could change how Percy views his father and their connection.
Maybe they would meet their ancestors. Percy could see his Greek hero predecessors and Artemis might interact with the first hunters she ever had. This could lead to some interesting exchanges, like learning forgotten hunting techniques or ancient combat skills.
One common theme is redemption. Percy often goes back in time to correct past mistakes, either his own or those of others, seeking a kind of redemption. For example, in some stories, he tries to save characters who died in the original timeline. Another theme is self - discovery. When he's in a different time, Percy learns more about himself and his powers. He might discover new abilities or a different side of his personality.