There might be. In the Naruto series, both Naruto and Nagato have complex backstories. If they were brothers in a fanfic, it would be really interesting. Maybe Naruto could have influenced Nagato to take a different path earlier. For example, Naruto's positive attitude towards life and his belief in peace could have rubbed off on Nagato, preventing him from going down the more violent routes he took in the original story.
Yes, there might be such fanfictions out there. Fanfiction writers often come up with unique family relationships for characters. In the Naruto universe, while it's not part of the official story, in fan-created works, Nagato could potentially be written as Naruto's uncle. This could add interesting twists to the plot, like exploring how Nagato's past and his connection to Naruto's family might change the way Naruto grows up or views the world.
One possible plot could be that they grow up together in a small village. Naruto's positive influence makes Nagato less likely to be influenced by Madara's ideas later. They both train under Jiraiya, and together they try to bring peace to the ninja world in a different way than in the original story.
Maybe Nagato had a relationship with an Uzumaki woman before he became fully involved in the Akatsuki. This woman could have given birth to Naruto but for some reason, Naruto was separated from Nagato at a young age. It could be due to the chaos and danger that Nagato was getting into with his plans for the Akatsuki.
He could be more light - hearted. Instead of being burdened by his past immediately, he might start off with a more positive outlook. For instance, he could be curious about the new world around him and approach things with a sense of wonder.
In some fanfictions, Naruto and Nagato might be related through their shared experiences with the ninja world. They both faced great tragedies. Naruto could be seen as a successor to Nagato's ideals in a way. Nagato once wanted peace through force, but Naruto shows that peace can be achieved through understanding and forgiveness.
Naruto's character could become more conflicted. He has always been about hope and friendship, but being related to Nagato might make him question his own beliefs. He might start to see the world in a more nuanced way, understanding that there are reasons behind Nagato's actions that he previously didn't fully consider.
Naruto might be more brooding. Since Nagato had a rather tragic past, Naruto could inherit some of that darkness. He may not be as openly optimistic as in the original story.
One possibility is that there was some sort of spiritual or chakra - based connection between Naruto and Nagato. Nagato, being the possessor of the Rinnegan, recognized Naruto's strong will and the fact that he was on a path to change the ninja world for the better. Through this connection, Nagato was able to transfer the power of the Rinnegan to Naruto. It could also be related to the nature of the Sage of Six Paths' power that was somehow involved in this transfer, as both Naruto and Nagato were related to the Sage in different ways.
In some fanfiction concepts, there could be a spiritual or mental connection established between Naruto and Nagato. Since Naruto has this unique ability to understand and connect with people on a deep level. Through this connection, Nagato might pass on the power of the Rinnegan to Naruto. It could be like a transfer of not just the physical power but also the knowledge and understanding that comes with the Rinnegan.