Maybe it's the Doctor's ability to travel through time and space. Percy, who has his own adventures in a world full of magic, might be fascinated by the Doctor's far - reaching travels.
The Doctor has a vast knowledge of different cultures and species across the universe. Percy, who is used to the complex world of Greek gods and monsters, might be drawn to the Doctor's even broader understanding. In fanfic, this could be a strong reason for Percy to be a fan of the Doctor as he could learn a great deal from him about the wider cosmos.
Yes, in some fanfics Percy Jackson could be depicted as a fan of the Doctor. Fanfic writers often create crossovers and unique scenarios where characters from different universes interact or have interests in each other.
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.
Perhaps he has been exposed to some sort of deadly and unknown substance in the mythical world. This could be a new type of monster venom or a strange plant that he accidentally ingested. The substance could be attacking his body from the inside, causing his internal organs to bleed, and thus he throws up blood.
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.
It could be due to some sort of poison or magical spell. In the Percy Jackson universe, there are all kinds of creatures and magic that could cause such a reaction. For example, if he was exposed to a slow - acting venom from a mythical beast, it might gradually make him faint.
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.
In some fanfictions, he might be exiled because of false accusations. Maybe someone frames him for a crime he didn't commit, like stealing a powerful artifact from the camp's vault. The camp leaders, believing the false evidence, have no choice but to exile him.
Another reason might be that she is forced to leave. There could be a magical or divine force at play. Maybe a god or goddess, who has some grudge against Percy or his father Poseidon, manipulates the situation so that Sally has no choice but to abandon Percy. This would add a lot of drama and conflict to the fanfic.
One possible reason could be power politics among the gods. Poseidon might see Percy as a liability in some complex power play. Maybe other gods are pressuring him to distance himself from Percy for some hidden agenda. Another reason could be a misunderstanding. Percy might have unknowingly done something that Poseidon misinterprets as a threat to his domain or power. For example, Percy's actions in the mortal world might have unintended consequences for the underwater realm.
One reason could be for a fresh take on the story. Writers might want to break away from the typical demigod narrative and explore a darker, more supernatural side of the Percy Jackson universe. Another reason could be to create a more complex and morally ambiguous character. By making him a demon, they can introduce new conflicts and relationships.