A new, mysterious deity could be the main antagonist. This deity could be from a different pantheon and feels threatened by the power of Zeus and his son Percy. So, they start causing chaos in the world of the Greek gods and Percy has to stop them.
Another option is a group of rogue demigods who are jealous of Percy's status as a son of Zeus. They form a secret alliance and plot to bring him down. They could be led by a demigod with a grudge against the gods in general and sees Percy as a symbol of their power.
It could be a powerful Titan who escaped from Tartarus and wants revenge on Zeus by targeting his son Percy. This Titan might have unique powers that make him a formidable foe.
A powerful Titan who sees Percy as a threat to his plans. Since Percy has the power of Zeus and Poseidon, he could potentially stop any chaos the Titan wants to create. The Titan might try to turn Percy's friends against him or find a way to strip him of his powers.
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.
Hera could be a main antagonist. Since she's often jealous and protective of Zeus, she might not be happy with Percy being adopted. She could try to undermine him at every turn. Another could be Ares. He might see Percy as a threat, especially if Percy starts to gain more power as Zeus' adopted son.
Some of the minor gods who feel overshadowed by Zeus and Hera might be antagonists. In this fanfiction, they could see Percy as a symbol of the over - dominance of Zeus and Hera. They might plot against Percy to send a message to his parents. These minor gods could use their unique powers and their knowledge of the magical world to create all sorts of problems for Percy, from cursing him to setting up traps in his path.
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.
Perhaps an ancient sea god who was once an enemy of Pontus. This god could see Percy as a threat because of his heritage. He would use his own minions, like sea serpents and murlocs, to attack Percy and those he cares about. He might also try to corrupt Percy, tempting him with power to turn against his friends.
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 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.
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.