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 ancient monsters that were once defeated by the gods could see Percy as a symbol of the new order they want to destroy. They might band together and target Percy specifically because of his connection to the gods as a consort. They could be led by a powerful and vengeful monster, like a resurrected Typhon. These monsters could use their strength and cunning to attack Percy from all sides, not only in physical battles but also by spreading rumors and fear among the demigods and the gods themselves, trying to isolate Percy so that they can finally defeat him.
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.
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.
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.
In Percy Jackson Gods Consort Fanfiction, writers can get creative with the powers and personalities of the consorts. They might show how these consorts interact with the demigods, like Percy. For example, a fanfic could depict a consort helping Percy on a quest in a way that the gods themselves couldn't. It gives a new perspective on the whole mythology - based world of Percy Jackson.
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.
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 power - hungry Atlantean noble who wants to rule not just Atlantis but also the surface world. He sees Percy as a threat to his plans and tries to stop him at every turn.
A new and powerful demon that has emerged from the darkest corners of the underworld. This demon is bent on using Percy's connection to the overworld to break through the barriers between the two worlds and unleash chaos. It has powers that are different from what Percy has faced before, like the ability to manipulate the very essence of the underworld's environment.
A powerful Amazonian sorceress who has turned against her own kind and is now trying to use dark magic to take over the world. She could see Percy as an obstacle in her path and constantly try to defeat him.