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.
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 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.
Well, he might find that his demigod powers work differently. Maybe in this new world, the water doesn't respond to him in the same way as in his own world. He could also encounter new and strange creatures that he has never seen before, and have to figure out how to deal with them without the help of his usual friends from Camp Half - Blood.
He might encounter new and strange creatures. In many fanfictions, Percy could meet unique magical beings that don't exist in his own world. For example, he could come across sentient plants that can communicate or floating islands with their own mini - ecosystems.
Conflict is a very common theme as well. There are often conflicts between Percy and the new characters he meets, either because of misunderstandings or because they have different goals. And there's also the overarching conflict of Percy trying to find a way back home or to reverse his banishment. This conflict drives the plot forward and keeps the story exciting.
Another option could be Wattpad. Although it has a wide range of content, including many fanfictions. You can search for the specific 'Percy Jackson Banished' fanfiction there. Just be aware that since it has a lot of different types of stories, it might take a bit more effort to find exactly what you're looking for compared to more specialized fanfiction platforms.
One possible plot could be that in a world where the gods of Percy Jackson and the Avengers co - exist, Percy is somehow tricked or forced to banish the Avengers. Maybe there's a power struggle among the gods and they see the Avengers as a threat to their power, so they use Percy, who has a strong connection to the divine world, to get rid of them. Percy might be conflicted as he may admire the Avengers' heroism but has to follow the gods' orders.
In some fanfictions, Percy might be banished because he goes against the traditional ways of the demigod society too much. For example, if he tries to form an alliance with a group that the other demigods consider enemies. His actions could be seen as a threat to the stability of their world, so they banish him to keep the peace.
Well, perhaps the god in question has been misusing their powers and causing harm to mortals and demigods alike. Percy, being the hero he is, decides to take matters into his own hands and banish the god. After the banishment, Percy then has to find a way to fill the void left by the god. He might have to take on some of the god's former responsibilities, which is no easy feat as he is still just a demigod.