The gods themselves could be the main antagonists. Since they cursed Percy, they might be trying to keep him in a state of misery or use him for their own purposes.
It could be a demigod who is jealous of Percy. When Percy is cursed, this demigod sees an opportunity to take his place or get rid of him once and for all. They might manipulate the situation to make Percy's curse even worse.
A powerful monster could also be the main antagonist. The curse might have attracted the attention of this monster, and it could be hunting Percy down. It might see Percy as a weakened target due to the curse, or it could be that the curse has some connection to the monster's origin or purpose.
The main antagonist could be one of the major gods who cursed Percy. For example, Zeus might be angry with Percy for some reason and decide to curse him. Zeus would then use his power to send all kinds of obstacles and enemies Percy's way. He could manipulate the weather to create storms that target Percy or send powerful monsters after him.
The main antagonist might be a new character, a powerful being that rules the realm where Percy is banished. This being could see Percy as a threat to his or her power and try to stop Percy from finding a way back.
It could be an envious demigod who feels that Percy doesn't deserve his new position as a consort of the gods. This demigod might plot against Percy, trying to undermine his influence among the gods and the other demigods.
A group of rogue demigods who have turned against the gods and see Percy as a traitor for being so close to them. They form an alliance and try to stop Percy from fulfilling any quests or tasks given to him by the gods, and might even try to capture or kill him.
Set, the Egyptian god of chaos. He could be a great antagonist as he might see the combination of Greek and Egyptian powers in Percy and the other demigods as a threat to his own plans of spreading chaos. He could try to manipulate events to turn the two groups against each other.
Another possibility is a demigod who has turned against the other demigods and sided with a particularly cruel god. This demigod could have been corrupted by power or a desire for revenge, and they use their knowledge of the demigod world to help the god in the war. Percy would then have to face this former ally, which would be a very emotional and difficult conflict for him.
Another possibility is an ancient evil that has been awakened. This entity might see Hermione as a threat because of her potential power. So it curses her to stop her from growing stronger. In this case, the antagonist would be very powerful and mysterious, and Hermione and her friends would have to do a lot of research and exploration to find a way to defeat it.
Obviously, the gods themselves would be the main antagonists. Since they are the ones who kill Percy and Jason in this concept. It could be a group of gods, like Zeus, Poseidon, and Hera, who feel that the two heroes are getting too out of hand.
One possible plot could be Percy struggling to control new, strange powers that come with the curse. Maybe he has to constantly battle against the dark impulses the curse brings out in him.
It could be a descendant of one of the Death Eaters who holds a grudge against the Potter family. They might try to finish what Voldemort started and target Albus specifically.