Yes, there are likely some fanfictions out there with this concept. The Percy Jackson fandom is quite large and creative, so it's possible for fans to explore such an interesting and unorthodox relationship in their stories.
Well, sometimes in fanfiction, his brother might be a mortal who discovers his demigod heritage later. This could add an interesting twist to the story as he has to adapt to the world of gods and monsters. Or it could be a long - lost half - brother from a different camp, like a son of Poseidon from another part of the world who was hidden away for some reason.
There's a fanfiction called 'Brotherhood in Camp Half - Blood'. In this story, Percy's new brother is introduced in a very dramatic way. The author does a great job of showing how the brother fits into the world of Percy Jackson, with lots of action and adventure sequences. It also explores the relationship between the two brothers in depth, like how they deal with the challenges together and support each other in the face of danger.
Yes, there are some out there. One popular one might be on Archive of Our Own. It often delves into their relationship, exploring how Percy, as Achilles' brother, might interact within the world of Greek mythology. It could show them training together, facing challenges side by side, and how Percy might deal with the legacy of having such a famous brother like Achilles.
It can be considered normal. People often get interested in fanfiction for various reasons. In this case, Percy's brother might like Annabeth fanfiction because he admires her character traits in the original story. The fanfiction could offer new perspectives on her, or it might be that he simply enjoys the writing style of the particular fanfictions he reads.
One interesting Percy, brother of Loki fanfiction could be 'Percy's Asgardian Adventure'. In it, Percy discovers his relation to Loki and has to navigate the complex politics of Asgard. Another one might be 'Percy and Loki's Bond', which focuses on how their brotherly bond develops over time, despite the differences in their upbringing. There's also 'Percy in Loki's Shadow', where Percy struggles to come out from under Loki's well - known reputation in Asgard.
A fanfic about Percy, brother of Zeus, could start with Percy feeling a sense of isolation. Despite being part of the divine family, he doesn't quite fit in. He decides to leave Olympus for a while and explore the mortal world. There, he experiences the joys and sorrows of humanity in a way that Zeus never has. He falls in love with a mortal, which causes a huge rift between him and Zeus. This love story could be the central theme of the fanfic, with Percy having to choose between his family and his new - found love.
They could interact in a very competitive way too. Maybe they compete in different tasks or challenges within the story. For instance, if there's a race to find a magical item, they both want to be the one to succeed first, but still have a deep underlying sibling bond. Percy might tease Zoe sometimes in a brotherly way, and Zoe would roll her eyes at his antics but secretly be fond of him. Their interactions would be a mix of typical sibling banter and deep emotional support for each other.
His character could develop in a way that he becomes more powerful. Since Kronos is a very powerful being, Percy might inherit some latent power. But he would have to learn to control it. He would also become more empathetic towards the Titans in a sense, as he realizes that Kronos is his brother. This could lead to him trying to find a middle ground between the Titans and the gods, which would be a major shift in his character from just being a defender of the gods.
His powers might become more related to fate - manipulation. He could, for instance, foresee certain events related to the destinies of people or creatures. This would give him an edge in battles as he could anticipate the moves of his enemies based on their fated paths.