There's a chance that it could be a character from Percy's family. For example, a distant relative who has been corrupted by some dark magic. They might betray Percy for their own gain or because they are being controlled, and this betrayal could lead to Percy being killed.
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.
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.
The gods, especially Zeus. He has always been a bit suspicious of Percy. In fanfiction, he could easily be written as spreading lies about Percy to the other gods and demigods, leading to everyone turning against him. Also, some new characters introduced in fanfiction might be the ones who start the chain of events that lead to Percy's all - around betrayal.
He may also try to figure out what went wrong. Percy is a smart demigod, and he would likely not just accept the betrayal without trying to understand the cause. So, he might start investigating, talking to other characters who might have some insight, like the other demigods or even some minor gods who are friendly to him.
The gods are always a possibility. Zeus, for example, has been distrustful of Percy in the past. If Zeus feels that Percy is getting too powerful or is a threat to his rule, he could engineer a situation where Percy is betrayed. He might use other demigods or even mortals to turn against Percy.
Perhaps she's a sister who was thought to be dead but actually survived. She could have been corrupted by the experiences she had while being 'dead'. When she returns, she blames Percy for not saving her properly. This false blame leads her to betray Percy. She could start spreading rumors about Percy being a coward or a bad leader among the demigod community.
One possible reason for Annabeth to betray Percy in fanfiction could be a misunderstanding. Maybe she was misled by false information about Percy's actions or intentions. For example, if someone spread rumors that Percy was secretly working against the demigods, Annabeth might believe it without getting the full story.
Another aspect could be that Percy is betrayed by a family member. For example, if it is revealed that a relative he trusted was working for an enemy all along. This would shatter Percy's world as family has always been important to him, and it would be a major plot point in the fanfiction, leading to his emotional and physical struggles.
They're popular because the idea of Percy being betrayed is a big contrast to his usual heroic image. Fans like to see how he would react in such difficult situations. It adds a new layer of depth to his character.