It could be an ancient deity that was banished long ago. Maybe a primordial god or goddess who was considered too powerful or too dangerous for the other Olympians. For example, it could be Erebus, the god of darkness.
I'm not sure if there's a specific existing fanfiction exactly like this. However, it would be a very interesting concept. Naruto's ninja skills combined with the mythological elements of being the son of Medusa and in the world of Percy Jackson could lead to some really unique adventures. Maybe Naruto could use his shadow clone jutsu to outwit the monsters from Percy Jackson's world, while also having some sort of snake - related powers from his Medusa heritage.
Well, it could be about Percy facing a new and powerful threat that even the Olympians can't handle easily. Maybe he discovers a hidden 13th Olympian who has been locked away for centuries and now is causing chaos.
Well, you could write a fanfiction where Percy loses his memory and has to rediscover his powers and his place among the demigods. Or perhaps a story about how the minor gods in the Percy Jackson universe form their own alliance because they feel overlooked by the Olympians. You could also create a fanfic that focuses on Annabeth's journey if she was separated from Percy and had to fend for herself in a dangerous situation.
In this fanfiction, it could be that Percy is chosen for a special task by the existing Olympians. They see his potential not just as a hero but as someone who could join their ranks. So he gets trained in Olympian magic and lore, which is very different from what he's used to. He has to learn how to control new powers and also deal with the politics among the Olympians.
In this fanfiction, the interactions would be full of surprises. Naruto, as the son of Kami, would bring a whole new level of power and culture to the table. The demigods would be both curious and cautious about him. Grover, for instance, might be a bit scared at first because Naruto's powers seem so different from what he's used to. But as they get to know each other, Grover could find that Naruto has a kind heart just like the demigods. Naruto would interact with the Percy Jackson characters in a way that combines his ninja training with his newfound identity as the son of Kami. He could use his speed and stealth to help the demigods in their quests, and in return, they could help him understand the complex world of Greek gods and demigods better. This exchange of knowledge and skills would not only strengthen their relationships but also create a more diverse and exciting story.
Fanfiction based on 'Percy Jackson: The Last Olympian' can be quite diverse. Some might focus on the relationships between the characters, like Percy and Annabeth's relationship evolving in new ways. Others could explore the idea of new threats emerging in the demigod world. It's also a great way for fans to connect with each other, sharing their ideas and interpretations of the story.
First, you should re - read the original books to get a good feel for the characters, the world - building, and the overall tone. Then, come up with an interesting concept or plot. It could be something as simple as a day in the life of a demigod that wasn't explored in the books. Next, start writing down your ideas for the characters' actions and dialogues.
The Titans might still be a threat. Even though they were defeated before, they could have some remnants or followers who don't want Percy to become an Olympian because it would strengthen the Olympian side even more.