Perhaps in the fanfic, Pein gives Naruto the Rinnegan to create a balance of power. With the Rinnegan, Naruto might face new enemies who are after this powerful dojutsu. He would then have to use his newfound power, along with his existing skills like Sage Mode and Rasengan, to protect his friends and the village. The story could also explore how Naruto's view of the world changes with this new power.
He would become more introspective. The Rinnegan has a lot of history and power, and Naruto would have to understand its origin and how to use it properly. This could lead to him maturing faster, as he now has a greater power to protect those he loves. He might also become more of an enigma to his friends as he delves into the secrets of the Rinnegan.
Well, one possibility is that Naruto gains new powers with the Rinnegan. He might use it to finally bring true peace to the ninja world. Maybe he could combine the power of the Rinnegan with his existing Sage Mode and Nine - Tails chakra, becoming an even more formidable force against any threats.
The story would change drastically. Naruto's combat abilities would be enhanced. He could use the Rinnegan's powers like the Six Paths techniques, which would give him an edge in battles. For example, he could use the Preta Path to absorb chakra attacks from opponents.
It's possible that the Sage of Six Paths has some sort of plan from the afterlife. He manipulates events so that Pein's Rinnegan goes to Naruto. This could be because the Sage foresees a great threat to the ninja world and believes Naruto with the Rinnegan can be the savior. The transfer might occur during a spiritual encounter between Naruto and Pein, where the Sage's influence is at work.
The plot could take a turn where Naruto is hunted by those who want the Rinnegan for themselves. Orochimaru might be very interested in Naruto's new power. Also, other villages might see Naruto as a threat. This would force Naruto to either hide his power or use it to assert his dominance. It could also change his relationship with Sasuke, as Sasuke has his own power goals, and Naruto's Rinnegan might either make Sasuke more competitive or more willing to team up with Naruto.
Well, the plot implications are many. Firstly, Naruto's new power might attract new villains who are interested in the Rinnegan. This could lead to new and more dangerous threats. Secondly, it could change his role in the village. He might be seen more as a god - like figure, which could create some jealousy or resentment among some of the villagers. And within the ninja world, the other Kage might have to reevaluate their stance towards Naruto and his village. It could also lead to Naruto exploring new places or dimensions that are related to the powers of the Rinnegan.
One popular 'Naruto and Fem Pein fanfic' is 'The World of a Female Pain'. It explores an alternate universe where Pein is female and her interactions with Naruto are quite interesting. It has a unique take on the characters' relationships and the overall Naruto universe.
The plot could involve the child trying to understand Pain's actions. Maybe the child is born after Pain's death and has to face the consequences of his father's actions in the ninja world.
I'm not sure about a specific 'child of pein naruto fanfic'. But you can try searching on fanfic websites like Fanfiction.net or Archive of Our Own. There are a large number of Naruto fanfics there, and you might be able to find one related to this concept.