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.
Well, it depends on the specific fanfic. There are a vast number of Naruto fanfics out there. Some writers might be creative enough to come up with a plot where Naruto somehow acquires Madara's Gunbai. It could be through a strange encounter, a time - travel situation, or some other fictional device. This can lead to really exciting storylines as Naruto would then have to figure out how to use this new weapon and how it affects his existing powers.
In such fanfiction, Sakura might be depicted as more alluring and perhaps more bold in her interactions with Madara. Madara could be shown as having a certain charm that draws Sakura to him.
Well, it could be through his powerful ninja techniques. Maybe he uses his Sharingan to paralyze Sakura, or perhaps he physically restrains her with his great strength. In fanfictions, there are many creative ways for such a scenario to play out.
Madara could also save Naruto by using his knowledge of the ninja world. Maybe he has some inside information about a plot against Naruto and he intervenes in time to stop it. He might have discovered a secret plan by an enemy group and takes action to keep Naruto out of harm's way. This could involve manipulating events behind the scenes or directly confronting the threat.
Naruto is often paired with Madara in some fanfictions. Their interactions can be really intense, as Naruto tries to either convince Madara to change his ways or fight against his reborn form.
Naruto might first struggle to understand the power of the fan. Since it was Madara's, it could have dark and complex powers. He may have to train himself to control it, perhaps with the help of Kakashi or Jiraiya (if he were still alive).
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.
Perhaps he sees her as a threat. Sakura is a skilled kunoichi, and Madara may want to prevent her from interfering in his plans. So he restrains her to keep her out of the way.
Well, in some versions of fanfiction, Naruto might have unlocked a new and super - powerful form of his Sage Mode. This enhanced form could give him the strength and speed necessary to outmaneuver and overpower Madara. Maybe he also gets some unexpected help from allies, like a new jutsu from Kakashi that weakens Madara's defenses just long enough for Naruto to land the final blow.