Perhaps an ancient sea god who has a grudge against Thetis. This god sees Percy as a way to get revenge on her. He could send all kinds of sea - based disasters and creatures to attack Percy and his friends. He might also try to corrupt Percy and turn him against his own values.
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.
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.
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.
A possible main antagonist could be Eris, the goddess of strife. She might be jealous of Aphrodite's beauty and power and see Percy as a tool to disrupt Aphrodite's plans. Eris could send her minions to create chaos and conflict between Percy and Aphrodite, trying to make them turn against each other.
One idea could be Percy going on a quest to find a lost artifact that was once Thetis'. He could face various sea monsters along the way. Another plot could be Percy having to prove himself worthy in the eyes of Thetis' family. Maybe he has to pass a series of trials in an underwater realm.
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 an ancient evil god who manipulates Percy into betraying the son of chaos. This god might have a long - standing grudge against the son of chaos or his lineage and sees Percy as a useful pawn.