Well, the main antagonists could be a group of rogue demigods who have formed a cult around Kronos. They believe that Percy, as the heir of Kronos, should lead them in overthrowing the current order of the demigod world. But Percy doesn't want any part of it, so they become his enemies. Another possible antagonist could be an ancient being that was once in league with Kronos and now sees Percy as a means to resurrect Kronos or continue his dark legacy. This being would stop at nothing to force Percy to embrace his role as the heir.
The other Titans could be main antagonists. For example, Hyperion who is known for his great strength and his desire for destruction. He might not fully trust Percy and constantly try to undermine him in Kronos' eyes. Another could be Atlas, who is already a major foe in the Percy Jackson series. He might see Percy as a threat to his own plans within Kronos' regime.
In this fanfiction, it could be some of the Titans who are still loyal to Kronos' old ways. They might see Percy as a tool to bring back Kronos' full power. They would try to manipulate Percy into joining their cause, and when he refuses, they become the main antagonists trying to either kill him or use his power against his will. Another possible antagonist could be a powerful demigod who is jealous of Percy's new - found status and wants to take it for himself.
The Olympian gods could be the main antagonists. Since Percy is the adopted son of Kronos, they might see him as a potential threat and try to stop him before he can fulfill any of Kronos' possible plans. They may send their demigod heroes after him.
Some of Kronos' minions, like the monsters he commands, could be antagonists. For instance, the dracaenae. They are always eager to prove themselves to Kronos and might see Percy as competition within Kronos' ranks. They could constantly try to undermine Percy's position and cause trouble for him.
Other demigods who are power - hungry could also be antagonists. They might envy Percy's new connection to Nyx and try to undermine him at every turn. They could form alliances against him and plot to steal his powers or his status as the heir.
It could be the Titans who see Percy as a threat. Since he is the son of Kronos, they might want to either use him for their own purposes or eliminate him to prevent any interference in their plans.
The Giants might also be antagonists. They could band together and target Percy's kingdom, believing that by destroying him and his rule, they can undermine the power of the gods further. They might use their brute strength and strategic thinking to attack Percy from different fronts.
Another option could be a group of rogue demigods who have turned to the dark side. They follow Percy to Forks, hoping to find some powerful artifacts there. They don't care about the vampires or werewolves and are willing to cause destruction to get what they want. Percy has to stop them while also dealing with the local supernatural creatures.
Obviously, Percy is the central character. As the heir of Kronos, he is the focus of the story. His friends like Annabeth are also important characters. Annabeth often serves as Percy's moral compass, trying to keep him from fully succumbing to the dark influence of his new heritage. Grover might also be there, providing his usual support and comical relief.
The Titans could be the main antagonists. Even though they have been defeated before, some of them might have found a way to return or their followers could be causing trouble. They see Artemis as a threat or a target for their revenge against the gods. Another possibility is a new group of powerful monsters that have banded together and are specifically targeting Artemis for her power and influence among the demigods.