Yes, there are some great ones. You can check out fanfiction platforms like Archive of Our Own. Look for stories with high ratings and positive reviews. Some might focus on Percy's adventures in a world that combines the mythologies related to Achilles and Percy Jackson.
In 'Percy son of Achilles fanfic', the theme of legacy is quite prominent. Percy has to carry the legacy of Achilles, which can be both a burden and a source of strength. Another theme is friendship. His friendships with other characters might be tested or strengthened because of his new identity. And there's also the theme of discovery. Percy discovers new things about himself, his powers, and his place in the world because of being the son of Achilles.
If Percy was the son of Achilles, his relationship with Annabeth might become more strained. Percy could become more headstrong and impulsive because of the influence of Achilles' traits, which would clash with Annabeth's more strategic and cautious nature. For example, in battle situations, Percy might rush in without a proper plan, causing Annabeth to worry more about his safety and get frustrated with his new behavior.
One interesting plot twist could be that Percy discovers he has some of Achilles' more negative traits along with his powers. For example, Achilles was known for his pride, and Percy might start to struggle with excessive pride that gets in the way of his relationships with his friends at Camp Half - Blood. Another could be that the gods, fearing Percy's new connection to Achilles, send out a series of trials that are specifically designed to test his loyalty and his ability to control the power of Achilles. Maybe he has to face off against a powerful monster that can only be defeated if he uses his Achilles - like invulnerability in a very specific and dangerous way.
In this fanfic, Percy's character could develop in several ways. Firstly, his understanding of power and responsibility might deepen. With the Curse of Achilles, he has a significant advantage, but also a great burden. He may become more cautious in his actions as he doesn't want to misuse the power of the curse. Also, his relationships with other characters may change. Some might be in awe of him, while others may be jealous, which could lead to him becoming more discerning about who he trusts.
It could be an old enemy of the gods who sees Percy as a threat because of the Curse of Achilles. Maybe a Titan who escaped from Tartarus and wants to use Percy's power for their own gain. If they can control Percy, they could have a powerful weapon against the gods.
Well, in this fanfic, perhaps there are unique interpretations of the Curse of Achilles. It could be that Percy discovers new aspects of the curse that weren't in the original story. For example, it might have some sort of connection to his demigod powers in a way that makes him even more special. Also, the fanfic might explore how Percy deals with the knowledge that he has this powerful and potentially dangerous curse.
A great plot could involve Percy having to deal with the psychological impact of the Curse. He might start to feel overconfident and make mistakes. Then, his friends have to help him realize that the Curse is both a strength and a potential downfall. For example, he could be lured into a trap by an enemy who plays on his new - found sense of invulnerability.
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.
In the fanfiction of the Curse of Achilles in Percy Jackson, many authors like to play with the idea of Percy's vulnerability. Even though he has the curse which makes him almost invincible, there are always ways around it that the fanfic writers come up with. This could be related to his emotional state or some hidden loopholes in the magic of the curse.