There's also 'Percy's Quest for Identity'. This story delves deep into Percy's struggle with his identity as the son of Zeus and Metis. It shows how he tries to fit into the demigod world while dealing with the expectations that come with such powerful parents. It's really interesting as it explores his relationships with other characters like Annabeth and Grover in this new context.
You should also consider the character of Percy. What kind of person would he be with these new parentage? Maybe he's more confident or has different powers. Outline your story. Decide on a central conflict, like Percy having to face a new threat that targets him because of his Zeus - Metis heritage. And don't forget to add some of the signature elements of the Percy Jackson series, like the camp and the quests.
Obviously, Percy Jackson is one of the main characters. Since it's about him being the son of Metis, he would be central to the story. Then there might be other demigods like Annabeth who could be involved, perhaps helping Percy on his journey related to his mother.
One interesting plot could be Percy's journey to discover more about his mother Metis. Maybe he uncovers hidden powers or a secret prophecy related to her. Another could be his interactions with other demigods who also have a connection to Metis in some way, leading to new alliances and adventures.
One idea could be Percy having to mediate between Zeus and Hades during a major feud. Since he's the son of both in this fanfiction, he has a unique connection to them. He could use his powers and his knowledge of both of their domains to try and broker peace.
Yes, there are quite a few interesting ones. You can start by looking on fanfiction platforms like Archive of Our Own. Some fanfics might explore Percy's relationship with his divine parents in unique ways, or perhaps put him in new and exciting adventures that are different from the original series.
In this kind of fanfiction, Percy might challenge Zeus over issues like the unfair treatment of demigods. For example, Zeus could be overly harsh on demigods who make minor mistakes while the gods themselves get away with much worse. Percy, being a hero, would stand up for his fellow demigods.
In a fanfiction, Percy as the son of Zeus and Hades could have a very conflicted personality. He would be torn between the light and airy nature of Zeus's domain and the dark and brooding nature of Hades's. This internal struggle could be a major part of his character arc, as he tries to find a balance between the two aspects of his heritage.
One possible plot could be Percy's struggle with his new identity as the adopted son of Zeus. He might face envy from other demigods who don't understand why he was chosen. He could also have to deal with Zeus' overbearing nature as he tries to train Percy in godly powers. And there would likely be new quests that involve both his ties to Poseidon and his new relation to Zeus.
If Naruto was the son of Zeus in a Percy Jackson fanfiction, his character would have to adapt to a whole new world. The demigod world of Percy Jackson has its own rules and politics. Naruto, being used to the Hidden Leaf Village's system, would have to learn about cabins, quests, and the whole Greek mythology aspect. His shadow clones could be used in really creative ways during quests, like scouting ahead or fighting multiple monsters at once. And his ability to never give up would be a great asset when facing the many challenges that come with being a demigod.