Yes, there are likely some fanfictions with this concept. Fanfiction writers often come up with unique and creative ideas, and the idea of Naruto having some sort of special connection or relationship with Kaguya Otsutsuki in a fan - created story is not unheard of. It could involve Naruto exploring Kaguya's past, or perhaps having a role in her redemption in the fanfic's alternate universe.
A common theme is power discovery. Sakura often discovers new powers related to the Otsutsuki in these fanfictions. For example, she might unlock some unique abilities that are connected to their ancient lore.
One possible plot could be that Naruto discovers he has some hidden Otsutsuki bloodline. This leads to him being ostracized by some in the village who fear his new - found power. He then has to go on a journey to learn about his Otsutsuki heritage, facing challenges along the way and also having to prove that he's still the same Naruto at heart.
One great 'Naruto Kaguya Otsutsuki Fanfic' is 'The Legacy of Kaguya'. It explores her backstory in a very detailed way. It shows how she came to be the powerful being she was in the Naruto series. The author does a great job of creating new scenarios that fit well with the existing Naruto lore.
One interesting otsutsuki fanfiction could be about an otsutsuki who decides to live among humans and tries to understand their emotions. This otsutsuki might start to form relationships with humans, which is a big change from their usual aloof nature.
One possible plot could be that Naruto discovers he has Otsutsuki blood in him. This could lead to him having new and uncontrollable powers that he has to learn to master. He might be shunned by some in Konoha who fear his newfound abilities, while others see it as an opportunity for Konoha to become even stronger. Naruto would then have to struggle with his identity and prove that he is still the same Naruto they know and love.
Kaguya Otsutsuki is often very popular. As the progenitor of chakra, she has a lot of mystery surrounding her, and fanfiction writers like to explore her backstory further, perhaps giving her more complex motives for her actions in the original story.
One interesting concept is the exploration of the Otsutsuki clan's ancient powers. Fanfictions often delve into how these powers could be harnessed or misused. For example, a story might show a character learning to control the unique dojutsu of the Otsutsuki in new and unexpected ways.
The plot could involve Kaguya's influence on the OC. Maybe the OC is a new being in the Naruto universe and Kaguya sees potential in them. For example, she could want to use the OC to regain her full power or to create chaos in the shinobi world again. The OC might initially be in awe of Kaguya but then realize her true intentions and have to fight against her.