It could be one of Kronos' old allies who feels betrayed that Percy is now in a position of power. Maybe someone who was promised a lot by Kronos but didn't get it.
Another possibility is a demigod who is jealous of Percy's connection to Kronos. This demigod might believe that they deserve that power or heritage more. They could start causing trouble for Percy by turning his friends against him or sabotaging his quests. They would be a more unexpected antagonist compared to the Titans or Kronos' old allies, and their knowledge of the demigod world would make them a tricky enemy for Percy to deal with.
The main antagonist could be a powerful Titan who was imprisoned by Kronos long ago and now wants revenge. They see Percy as an extension of Kronos and target him. This Titan could have unique powers that make them a formidable foe for Percy. For example, they might be able to manipulate time, which would make battles very difficult for Percy as he tries to figure out how to counter such a power.
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 main character is surely Percy Jackson. But in this 'son of kronos percy jackson fanfic', new characters might be introduced that are related to Kronos' side of the story. However, the classic characters like Annabeth Chase are bound to be there too. She would be crucial in Percy's journey as she often is in the original stories. Grover Underwood, Percy's satyr friend, would also be a mainstay. His loyalty and friendship with Percy would be tested and explored in this new narrative where Percy has this unexpected connection to Kronos.
A great antagonist could be a Titan who has a grudge against Zeus and sees Percy as an easy target to get back at him. For example, Atlas. He could try to use Percy to free himself from his burden again or trick Percy into doing something that would cause chaos among the gods. Another option is a powerful and vengeful demigod who feels that Percy, as the son of Zeus, has been given too much power and attention, so he wants to take Percy down.
The main antagonist could also be an ancient and powerful spirit from the underworld that was sealed away long ago. Percy's presence as the son of Hades accidentally awakens this spirit. The spirit then starts to spread darkness and despair throughout the world of the demigods, and Percy has to find a way to stop it before it's too late.
A new and powerful Titan who has been hiding and gathering strength all this time. He could be jealous of the Olympians' power and wants to take over. Percy would have to figure out his weaknesses and stop him before he causes too much destruction.
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.
A group of rogue sky spirits might serve as the main antagonists. They are jealous of Percy's status as the 'Son of the Sky' and want to steal his powers. They could be constantly causing chaos in the sky, like creating dangerous storms and attacking flying creatures. Percy would have to figure out their motives and stop them before they cause too much damage. These sky spirits could have their own hierarchy and leader, making them a formidable foe.
Perhaps an ancient and evil creature that has a grudge against Oin. Since Percy is Oin's son, this creature targets him. It could be a monster that was once defeated by Oin and now wants revenge by going after his son.
Another option could be a corrupted demigod. Maybe a child of a minor Egyptian god who is jealous of Percy's status as Son of Sobek. This demigod could form an alliance with some dark forces and try to undermine Percy at every turn, creating all sorts of challenges for him.