It could be an ancient and powerful Titan who was thought to be defeated long ago. Since Percy is in the past, this Titan could be in his prime and see Percy as a threat to his plans of ruling over the world again. For example, Kronos might be even more powerful in this past era and Percy has to find a way to stop him without the help of his modern - day friends.
A powerful and evil demigod from the past could be the antagonist. This demigod might be jealous of Percy's knowledge and skills from the future and wants to use them for his own dark purposes. He could constantly try to undermine Percy and steal his secrets, all while trying to gain more power in the past world.
Maybe the main antagonist is an ancient primordial being that has been awakened by Percy's time - traveling. This being doesn't like the interference in the past and wants to erase Percy from existence. It has powers that are beyond what Percy has ever faced and he has to figure out how to defeat it using only the resources available in the past.
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.
Another possibility is a demigod from the past who is jealous of Percy's knowledge and power. This demigod could be someone who was once in a position of power or influence but feels threatened by Percy's sudden appearance and her attempts to change things. They might try to undermine her at every turn, whether by spreading false rumors about her or directly attacking her when she least expects it.
Even some of the ancient demigods who turned bad could be antagonists. They might see Percy as a threat to their power or plans in the past. They could have different values and goals compared to Percy, leading to conflicts. For example, a demigod who was power - hungry and wanted to use time - travel to change things for his own gain, and Percy would have to stop him.
Perhaps one of the Titans who were banished to Tartarus. They might see Percy as a threat to their plans of revenge or escape. Kronos, if he still has some form of existence in Tartarus, could be a major antagonist. He would have his own motives and powers, and he could try to manipulate Percy or simply get rid of him.
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.
He could meet his younger self. This would be a really interesting encounter as he could either try to guide his younger self or be shocked at how different he was back then. Another possibility is meeting some of the ancient heroes that he only heard about before. For instance, he might come across Hercules and learn from him.
It could be another character who also has some time - related powers but uses them for evil. This character might try to steal Percy's time - controlling ability or use their own powers to disrupt the timeline for their own gain.
Cell could be a great antagonist. Even if Gohan goes back in time, Cell might still find a way to exist. Maybe he adapts his plan to absorb the Androids earlier in time. Gohan would then have to face a more powerful and unpredictable Cell, who could potentially change the timeline to his own advantage.
Frieza would be a great antagonist. If Goku goes back in time to a point before Frieza was defeated, Frieza could be an even more menacing force as Goku might not have all the power - ups he had in the original timeline. He'd have to rely on his wits and basic training more.
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.