Well, in such a fanfiction, there could be a lot of conflict. Percy Jackson is from a world where Greek mythology rules, and Naruto has his own shinobi world. If Naruto is the son of Medusa, he might face discrimination in the Percy Jackson world because of his relation to a 'monster'. On the other hand, his ninja training could give him an edge in battles against the various creatures in that world. For example, his ability to move stealthily like a ninja could be useful when sneaking up on a harpy or a minotaur.
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.
The main character is Percy Jackson. Alongside him, we may have some characters that are exclusive to the fanfiction world. For example, there could be a character who is a half - human half - stone being as a result of Medusa's powers in the past. This character could be an ally or an enemy to Percy. Then there's a good chance that Chiron, the centaur trainer at Camp Half - Blood, will be in the story. He's always been a guiding figure for Percy, and in this new context, he'll have to give Percy advice on how to handle his new identity as the 'Son of Medusa'.
One interesting plot could be Percy having to face off against Medusa's other children in a battle of wits and strength. Maybe they are out to prove themselves as worthy as Percy, who has the fame of being Poseidon's son. Another could be Percy having to deal with the stigma of being 'Son of Medusa' in a world that fears her so much. He might have to constantly prove he's not a monster like his 'mother' is perceived.
You can develop Medusa by exploring her backstory more. Maybe show how she was before she was cursed, her hopes and dreams. For example, she could have been a beautiful and kind - hearted maiden once. Also, give her some complex emotions like regret for the people she has turned to stone.
Naruto's chakra control could be seen as a form of magic in the Percy Jackson world. His ability to create shadow clones could be used for various purposes, like scouting or confusing enemies. Since he's the son of Medusa, he might also have the power to petrify enemies at will, which would be a very powerful ability in battles against the monsters in Percy Jackson's world.
In fanfiction, the Son of Aphrodite could also have an interesting love life. Since Aphrodite is the goddess of love, her son might have a complex relationship with love. He could be a hopeless romantic, constantly falling in and out of love. Or he might be cynical about love, having seen the chaos it can cause, especially among the demigods.
It could be a demigod who has been corrupted by the power of Medusa's severed head. He uses the petrifying power for his own evil gains, like trying to turn all the other demigods into stone so he can rule the demigod world alone.
Sure, there are Percy Jackson and Medusa love fanfictions. Writers in the fanfiction community like to explore unusual pairings. They might rewrite Medusa's character to make her more sympathetic or create a whole new backstory for their relationship. But it's not a common or mainstream concept within the overall Percy Jackson fandom.
In a fanfic, perhaps Percy and his friends accidentally stumble upon Medusa's lair while on a quest. But instead of immediately attacking, Medusa offers them a deal. She says she will give them a valuable clue to complete their quest if they help her get revenge on one of the minor gods who wronged her in the past. Percy and his friends then have to decide whether to trust Medusa or not.
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.
The plot could involve a quest. For example, a powerful artifact has been stolen and scattered across different realms. Percy Jackson has to search in the world of Greek mythology, Naruto in his ninja world, and the Son of Artemis in the realm related to Artemis. Eventually, they realize that they need to combine their efforts. They could face various obstacles along the way. Percy might have to deal with sea monsters while Naruto battles ninjas from other villages who also want the artifact, and the Son of Artemis has to fend off mythical beasts in his realm.