One aspect could be that in many Percy Jackson - related fanfictions, Percy being betrayed by the gods often leads to a complete shift in his character arc. He might become more cynical or distrustful. For example, he could start to question his previous heroic deeds and wonder if he was just a pawn in the gods' games all along.
Apollo might be the betrayed god. He could have been tricked by another god into betraying Percy. For example, Apollo might have been promised more power or a higher status among the gods if he turned against Percy. But then he realizes too late that he's been used and that he's actually betrayed someone who could have been an ally.
Percy might feel a deep sense of hurt. He values friendship highly, and this betrayal would make him question who he can trust. He could become more guarded and less likely to trust new people easily. Reyna would be more focused on the bigger picture. She would see the betrayal as a threat not just to herself but to the stability of the demigod world. So she would start gathering her allies, those who still believe in her, and form a strategy to counter the false accusations and the forces behind the betrayal. She would be determined to prove that she and Percy are not the traitors they are made out to be.
At first, Percy would likely be angry. He's a fighter, and being betrayed by someone he loves would fuel his rage. He might go after Annabeth to demand an explanation. But as the reality sinks in, he could become very sad and withdrawn. He might isolate himself from his other friends as well, feeling like he can't trust anyone anymore. He would constantly be thinking about what he did wrong to make Annabeth turn on him.
He could be angry. Percy might lash out at those who betrayed him, feeling a deep sense of injustice. He would probably be determined to prove his innocence and get revenge on those who wronged him.
Percy might initially feel a great deal of anger. He's been wronged by those he thought were his friends. But then, with Annabeth by his side, he could start to focus on finding out the truth. He might use his skills, like his combat abilities and strategic thinking, to figure out who or what is behind the betrayal.
In some fanfictions, Annabeth might betray Percy for power. Maybe she gets lured by some dark force offering her great power and in order to get it, she has to turn on Percy. It could also be due to a misunderstanding. For example, she might be tricked into believing Percy has done something really bad and as a result, she betrays him without realizing the truth.
Perhaps Percy's loved ones are made to believe false rumors about him spread by an unknown enemy. As a result, they turn their backs on him. Percy would need to find a way to expose the real culprit behind the rumors and regain the trust of his friends and family.
Well, in many 'Percy betrayed' fanfics, the story usually starts with an event that makes Percy feel isolated. For example, in some, his friends might believe false rumors about him. 'Percy's Lonely Path' is a fanfic where he is shunned by his demigod comrades due to a misunderstanding. It shows his journey of trying to clear his name and deal with the pain of betrayal. These fanfics often play with the idea of loyalty and how easily it can be broken in the Percy Jackson universe.