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.
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.
Well, he might face a lot of challenges. Alaska is a cold and harsh place. He could encounter new mythical creatures that are native to that region in the fanfiction. Maybe he has to find a way to survive the extreme cold while also dealing with any enemies that banished him there in the first place.
In the fanfiction, if Percy gets banished to Tartarus, he could potentially meet some old enemies who have been banished there too. Maybe he'd have to team up with some unlikely allies to find a way out. It would be a struggle for him, as Tartarus is a place where hope is almost non - existent. He'd also have to deal with the harsh environment, like the rivers of fire and the jagged rocks.
One interesting plot could be Percy being banished to a forgotten realm and having to find his way back while facing new and unknown monsters. He might discover hidden powers within himself during this journey.
He might rely on his skills and the powers he already has. His control over water could help him find sources of water in Tartarus for survival. Also, his combat skills would be crucial in fending off the various monsters there.