Maybe it could be due to some powerful magic or a unique prophecy. In many fanfictions, unexpected events like this are often triggered by such elements.
In a fanfiction of Percy as the Father of Chaos, he could be in a constant struggle between maintaining order within the chaos he controls and letting the chaos run wild. His relationships with other gods and mortals would be very interesting. For example, some might fear him while others might try to gain his favor. He could also have a special connection with certain elements in nature that are associated with chaos, like storms or wildfires.
Well, if Percy is the father of Zoe in fanfiction, it might mean that there are some hidden powers or abilities that Zoe could inherit from Percy. This could be a major plot point. Also, their relationship could be full of emotional turmoil. Percy, being the protective father, would have to deal with all the dangerous situations that Zoe gets into, just like he does with his other friends in the original stories.
Well, in this fanfiction, it could be that the author wanted to explore a different side of Percy's character. Being the 'Father of the Primordials' might mean he has the power to shape the very essence of the world in this fictional universe. It might also lead to some really interesting plot twists, like how he interacts with the existing gods and demigods, and how they react to his new - found status. It could also introduce new enemies or allies based on his role as the progenitor of the primordials.
One idea could be that Percy discovers he has a long - lost connection to Thalia. Maybe in a magical twist, a prophecy reveals that he is fated to be like a father figure to her. He could then use his powers and experience to train Thalia, much like Chiron trained him.
In a fanfiction, Percy could become Annabeth's father in a magical realm where the rules of family and time are distorted. Maybe a powerful god or goddess messes with their destinies. Percy would then have to navigate the new relationship while still dealing with his own heroic duties. He might struggle to balance protecting her as a father and respecting her as an independent demigod who is used to taking care of herself.
I'm not sure if there is such a specific fanfiction with that exact title. Fanfiction can cover a vast range of themes and ideas, but this seems like a rather unique and perhaps not very common one. It might be difficult to find, if it exists at all.
In most of the Percy Jackson canon, Poseidon is Percy's father, and Athena has no relation to Percy in that way. But in fanfiction, anything can be reimagined. Maybe a powerful magic or a strange prophecy could be the reason. It could be a completely new take on the mythology, where the author decides to break the normal rules and create a unique scenario for Percy to be in such an unexpected role.
Yes, there are fanfictions with this concept. Writers like to explore unique family relationships in fanfiction, and the idea of Loki being Percy's father can lead to really interesting storylines. It can bring together different mythologies and create new adventures for the characters.