One possible plot could be Percy using his Uchiha heritage to gain new powers. For example, he might unlock the Sharingan which could enhance his battle perception in the demigod world. He could then use this newfound ability against his enemies, like the Titans or monsters. This would create a whole new dynamic in the Percy Jackson universe as he combines his demigod skills with Uchiha powers.
Yes, there might be such fanfictions out there. The Percy Jackson series and the Naruto world with Madara Uchiha are both quite popular, and fans often like to cross over different universes in fanfiction. It could be really interesting to see how Percy Jackson, with his own set of powers and personality from the Greek mythology - based world, would react to or be a fan of the powerful and complex Madara Uchiha from the Naruto universe.
Percy's power set would be different. Instead of just relying on his demigod powers, he would have access to Uchiha abilities. This would make him more complex in combat. He could be more strategic, using the Sharingan to analyze his opponents' moves before striking. Also, his relationships with other characters might change. Some might be afraid of his new powers, while others might try to use him for their own gain.
In a fanfiction, Madara Uchiha's grandson could have unique powers. Since the Uchiha are known for their Sharingan, perhaps he has an evolved form of it. He could use this power to protect the Hidden Leaf Village, or maybe he gets caught up in a conflict between different ninja clans who either want to use his power or are afraid of it.
In some fanfictions, it might be possible for Naruto to be portrayed as Madara Uchiha's grandson. Fanfiction often takes creative liberties and twists established relationships. However, in the original Naruto storyline, there is no such relation.
In most Naruto fanfiction, anything can be possible. However, in the original Naruto series, Naruto has no relation to Uchiha Madara in this way. But in some creative fanfictions, the author might create a complex backstory to make Naruto be Madara's grandson. Maybe they rewrite the history, or use some magic - like elements to connect them.
One implication could be a shift in Naruto's power source. Since Madara was extremely powerful, Naruto might inherit some of that raw power. Also, it could change his relationship with Sasuke, as Sasuke is an Uchiha. There might be more internal clan - related drama.
In fanfiction, the author could create a scenario where there was a secret relationship between an Uzumaki ancestor of Naruto and an Uchiha. This relationship could have been hidden for generations. And through some family secrets being revealed, it's discovered that Naruto is actually Madara's grandson. It could also involve some kind of genetic manipulation or curse that ties the two families together in a way that wasn't known before.
One way the story could develop is that Naruto would have an innate understanding of powerful Uchiha techniques. Since Madara was a master of the Sharingan and had many powerful jutsu. Naruto might be able to quickly master the Sharingan if he inherits it. For example, he could use it to enhance his combat abilities against stronger enemies. He could also have a different relationship with Sasuke. Maybe instead of being rivals, they could be more like cousins with a shared heritage to explore.
Try searching on AO3. It has a vast collection of fanfictions from various fandoms. Type in 'Percy Jackson' and 'Madara Uchiha' in different combinations in the search function. You might also check some Naruto - Percy Jackson crossover communities on social media platforms like Reddit or Tumblr. Sometimes, fans share links to their favorite or newly discovered fanfictions there. But it may take some time and effort to find exactly what you're looking for.