If Percy is thrown back in time, his powers could be enhanced. In the past, magic and the power of the gods were more prevalent. The very air might be charged with more divine energy. His ability to communicate with sea creatures could expand, as there could be species that are now extinct or have evolved in his own time. However, he might also face limitations. For example, if he goes back to a time when the gods were at war, some of his powers related to Poseidon might be restricted depending on his father's situation in that war.
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.
Percy might run into his old friends' ancestors. This could create some really strange and exciting interactions. For instance, if he meets an ancestor of Annabeth, he could learn things about her family history that she doesn't even know.
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.
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.
Maybe a corrupted past version of a demigod. For example, a demigod who was promised great power by the Titans and turned against the Olympians. This demigod could see Percy as an obstacle to their plans and try to stop him at every turn. They would know the time period well and could use that to their advantage against Percy.
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.
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.
His water - based powers might be affected in different ways. If he goes back to a time when the oceans were less polluted, the purity of the water could make his powers stronger. However, if he goes to a time when the gods were more in control of the elements, they might be able to limit his power. For example, Poseidon might have more say over how Percy can use water powers if they are in the same time period.
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.