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.
One popular 'Percy Jackson Banished Crossover Fanfiction' is 'The Banished God'. In it, Percy is banished to a different realm and has to find his way back while crossing over with characters from other mythologies. It has an exciting plot with lots of action and character development.
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, one idea for this crossover could be that Savitar somehow ends up in the world of Percy Jackson. Maybe he's chasing after some new kind of speed - the speed of a demigod? And Percy has to figure out how to deal with this strange, super - fast being who doesn't seem to follow the normal rules of the Greek myth world.
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.
Another idea is that Sophie Foster from KotLC travels to the Percy Jackson universe. She could be mistaken for a demigod at first. She would have to learn about the Greek gods and monsters. Her telepathic abilities would be really useful in the Percy Jackson world. For example, she could communicate with some of the monsters to find out their plans. And Percy and his friends would help her understand this new and dangerous world.