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.
Another possibility is that there's a prophecy in the fanfiction which states that Percy's presence will bring great destruction. Even if he hasn't done anything wrong yet, the fear of the prophecy coming true could cause the demigods or the gods to banish him. They might think it's the safest option to send him away rather than waiting to see if the prophecy unfolds.
Well, one reason could be that he's wrongly accused of a major crime against the gods. Maybe some false evidence is planted, making the gods believe he's a threat, so they banish him. Another reason might be that he's trying to protect someone or something, and his actions are misinterpreted as going against the gods' will. For example, if he's trying to save a powerful but 'forbidden' creature, the gods might see this as a violation and send him to Tartarus.
Maybe he accidentally breaks some ancient and unforgivable rule. For example, he could have uncovered a secret that the gods wanted to keep hidden and in their attempt to silence him, they banish him. In fanfiction, the writers often play with the idea of Percy's curiosity getting him into big trouble with the Olympians.
In some fanfictions, it could be that Percy has new, uncontrollable powers that the camp doesn't understand. They see him as a threat and banish him. For example, if he starts to show signs of a power that was once associated with an enemy of the camp. It's also possible that Percy's loyalty is questioned. If he befriends someone from an opposing group, the camp might think he has turned against them and banish him.
Well, perhaps in the fanfic, there's a prophecy that gets misinterpreted. The gods think Percy is going to cause great harm based on this wrong interpretation, so they send him to Tartarus. It could also be that there's some sort of power struggle among the gods. Percy might be caught in the middle of it, and one side decides to get rid of him by banishing him to Tartarus to tip the balance in their favor.
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.
Perhaps a prophecy misinterpretation. If a prophecy was misread and it seemed like Percy was the cause of great evil to come, the gods might take drastic action. For instance, if the prophecy spoke of a 'child of the sea' causing destruction, and they wrongly assumed it was Percy without fully understanding the context.
In fanfiction, Percy being rich might be a way for the writer to explore different aspects of the Percy Jackson universe. Maybe they want to show how the world of demigods would interact with wealth. It could also be a way to make Percy more like a modern hero, who often has access to a lot of resources. Plus, it can lead to comical situations where Percy, who is used to a more simple life, has to deal with the trappings of being rich, like dealing with butlers or managing a large estate.
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.
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.