A great plot idea would be Percy being sent back to a time when a great prophecy was first made in the Greek world. He could try to prevent or fulfill the prophecy depending on his understanding of how it would impact the future. Along the way, he would encounter ancient seers and have to figure out who to trust. He'd also have to deal with the fact that the magic and rules of that time were different from his own, adding an extra layer of challenge to his adventure.
One interesting plot idea could be Percy going back in time to the era of the Greek heroes. He could meet Hercules and learn from him. Maybe he would have to face the same challenges Hercules did, but with his own modern - day skills and knowledge. Another idea is that he goes back to the time when the gods first emerged and gets involved in the power struggles among them. This could change the entire course of mythology as we know it.
One idea could be that Percy goes back to the time when the gods first came to power. He could try to change the way the gods interact with demigods from the start, leading to a whole new world order for demigods. Maybe he'd teach the early demigods some of the skills he has, like advanced sword fighting techniques.
One idea could be Percy going back in time to the era of the Greek gods' creation. He could witness the birth of the first demigods and learn the true origins of his powers. Another plot could involve him traveling back to a time when a great prophecy was first made and trying to change the course of events to prevent a future disaster.
One idea could be Percy going back in time to the era of the first Olympian gods and having to deal with the raw, unbridled power of those early deities. He might find himself in the middle of a power struggle between Zeus and his father, Kronos, before the Titanomachy. Another plot could involve Percy trying to prevent a major disaster in the past that has far - reaching consequences in his own time. For example, stopping the release of a powerful monster that was supposed to be sealed away long ago.
Maybe Percy travels back to the founding of Camp Half - Blood. He could meet the first demigods and see how the camp was established. He could also learn ancient fighting techniques and bring them back to his time to use against modern enemies. This would add a really cool element of anachronism to the story.
One idea could be that the demigods are sent back to prevent a great disaster that was actually caused by one of their own kind in the past. They have to figure out who it was and stop it without changing too much of 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.
Jon Snow could be sent back to a time just before Ned Stark's father was killed. With his future - learned wisdom, he could try to save his grandfather and thus change the entire Stark family's fate. He may also discover secrets about his own lineage that were lost in time. This could lead to him having more power and influence in the past, as he might be able to claim certain rights or titles based on this new - found knowledge.
A possible plot is that Anakin is sent back in time and ends up meeting his mother again when she was younger. This encounter could give him a chance to save her from the Tusken Raiders, which might then have a profound impact on his emotional state and his path in the Force. He could also use this opportunity to train himself differently, perhaps learning from the Jedi of that era in a more positive way, without the strictures that later led to his disillusionment.
One idea could be Percy discovers a new power related to time during a quest. For example, he might be able to freeze time briefly to escape a dangerous enemy. Another could be that he travels back in time to change an event in the past that has a major impact on the present in the world of the Gods.
One idea could be Percy reliving the day he discovers his true identity over and over. Each time he tries different ways to break the news to his mom, like one time being super casual, another time making it a big dramatic reveal. Another plot could be him reliving a battle, and each loop he figures out a different strategy to defeat the monsters more efficiently.