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.
One common theme could be the idea of redemption for Medusa. Writers might explore how Percy's love could change her from a monster into something more. Another theme could be the forbidden love aspect, as their relationship goes against the norms of the Percy Jackson world.
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.
One idea could be Percy has to face Medusa again, but this time she has an army of stone minions. Another could be that Medusa was actually cursed by a more powerful god and Percy has to find a way to break it. Maybe Percy discovers Medusa has a long - lost relative who is being held hostage and he has to make a deal with her.
One idea could be Percy having to face Medusa in a new way that challenges his usual methods. Maybe he gets trapped in a dream where Medusa has the upper hand and he has to use his wits more than his sword. Another could be a scenario where Medusa is somehow redeemed and teams up with Percy against a greater evil. For example, an ancient monster that threatens both the mortal and mythological worlds.
One idea could be that Percy has to face a new threat from Medusa's long - lost sister who has even more powerful petrifying abilities. He has to use his skills and some newfound knowledge about the Gorgon lineage to defeat her.
One idea could be Percy using his water powers in a unique way against Medusa. For example, he could create a water shield that reflects Medusa's petrifying gaze back at her in a fanfiction. Another could be a scenario where Medusa, instead of being an enemy, teams up with Percy to face a greater threat.
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.
I'm not sure about extremely popular ones specifically for Percy and Medusa love. But often, on AO3, stories that have a lot of kudos and comments tend to be well - liked. You can sort the search results by these metrics to find the more popular ones.
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.