Yes, there are likely fanfictions with such a concept. The 'Percy Jackson' series has a huge fan base, and fans often come up with creative and out - of - the - box ideas. Some might explore the idea of Percy being born a primordial as it adds a whole new layer of depth and power to his character.
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.
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.
One possibility for a Percy Jackson fanfiction centered around the Primordial Son of Chaos could be a story where Percy discovers a hidden prophecy related to this powerful being. Maybe he has to team up with some unlikely allies, like a group of minor gods who are also interested in the balance that the Primordial Son of Chaos might disrupt or uphold. This could lead to a series of adventures across different realms, including Tartarus, where they search for clues about the true nature of the Primordial Son of Chaos.
I'm not sure it is a particularly popular fanfiction genre. While the Percy Jackson series has a large and passionate fanbase, the idea of him being 'born a primordial' is quite different from the established lore in the books. It could potentially be popular among those who like to explore very different interpretations of the character, but it's not likely to be as popular as fanfictions that stay closer to the main themes and storylines of the original series.
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.
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 common theme is the struggle between chaos and peace. Since the Primordial of Peace is involved, there's often a contrast with forces that want to disrupt the peace. Another theme is the discovery of new powers. Characters often find out they have some connection to the Primordial of Peace and have to learn to use these powers.