Another possibility is a group of outlaws or rebels in the banished world who don't trust Percy because he's from another place. They might think he's been sent to spy on them or take over. So they would constantly try to get rid of him. They could be very resourceful and know the ins and outs of the new world better than Percy, which would make them tough opponents.
It could be a rogue demigod who has a vendetta against Percy. This demigod might have spread the false rumors that led to Percy's banishment in the first place, and now he wants to make sure Percy never returns. He uses his own powers and manipulates other demigods and monsters to achieve his goal.
In a 'Percy Jackson banished to another world' fanfiction, Percy would be in for a wild ride. He could find that the laws of physics and nature are completely different. For instance, gravity might work in a strange way or time could pass at a different rate. His skills as a fighter and strategist would be crucial. He may have to learn new languages to communicate with the inhabitants of this new world. And he'd probably have to face his own inner demons while being away from his loved ones and the familiar places of his home world.
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.
A powerful sorcerer who also wants to claim the island for his own could be the main antagonist. He sees Percy as an obstacle to his plans and tries to eliminate him. The sorcerer might have control over some of the dangerous creatures on the island and use them to attack Percy.
The main antagonist might be an ancient and powerful being that has awakened. This being could see Percy and Annabeth as a potential threat to its plans of taking over the demigod world. So, it uses its influence to have them banished, thinking that without them, it would be easier to conquer. For example, a long - forgotten Titan who has found a way to break free from its prison.
A powerful sorcerer who has escaped from Tartarus and wants to use the chaos of the mortal world to regain his strength. He could be targeting Percy because Percy's presence in the mortal world disrupts his plans of secretly gathering power.
Maybe an old and powerful monster that has long been trapped in Tartarus could be the main antagonist. It sees Percy as a threat or a source of entertainment, and it tries to stop him from finding a way out or from getting stronger.
It could be a powerful wizard in the new world who sees Naruto as a threat to his rule. Since Naruto has unique powers from his own world, the wizard might want to eliminate him or use his powers for his own evil purposes.
It could be Ares. He is often portrayed as a violent and unpredictable god. Percy might banish him if he goes too far in causing wars and chaos among mortals. His banishment would have a huge impact on the battlefields of the mortal world.
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.