Well, in the fanfiction world, Minato might be overprotective of fem Naruto because he lost her once. Maybe there was some kind of incident in the past where Naruto was in great danger or even 'died' briefly. This made Minato extremely paranoid about losing her again, so he goes overboard with the protection. He might also be influenced by the fact that as a female in their world, Naruto could face different and perhaps more complex challenges than if she were male, like discrimination or special treatment from certain groups.
Well, Minato might constantly be by Naruto's side in the fanfiction. He could prevent Naruto from taking on any dangerous missions, even if Naruto is capable. For example, he may interfere when Naruto tries to join a risky battle against a powerful enemy, saying it's too dangerous for him.
One reason could be guilt. Since Minato wasn't there for Naruto when he was growing up in the original story, in the fanfiction, he might be overcompensating for that lost time. He feels like he has to make up for all those years he wasn't around to protect his son.
In a fanfiction, an overprotective Minato would be like a storm cloud over Sasuke and Naruto's relationship. Minato's actions, driven by his concern for Naruto, would constantly disrupt the natural development of Sasuke and Naruto's friendship. Sasuke would see Minato as an obstacle to his connection with Naruto. Naruto, while loving Minato, would also feel caged by his overprotectiveness. This could lead to a downward spiral in their relationship if not resolved. But if they all sit down and talk things through, it could transform into a more positive and understanding dynamic.
One possible plotline could be that Minato sees Sasuke as a threat to Naruto in some way, perhaps thinking Sasuke's pursuit of power might harm Naruto. So he constantly tries to keep them apart. But Naruto and Sasuke's bond is too strong and they resist Minato's overprotectiveness. Eventually, Minato realizes that their relationship is something that can't be broken and he should trust in Naruto's judgment.
Maybe it's because Gaara sees a lot of himself in Naruto. They both had difficult pasts and were kind of loners at first. Gaara wants to protect Naruto from the pain he once endured.
One possible scenario in this fanfiction could be that Naruto's sister constantly interferes in his ninja training. She might think the training is too dangerous for him and tries to stop him from taking on challenging missions. For example, when Naruto is about to go on a mission to the Land of Waves, his sister could try to convince the Hokage not to send him, believing that he's not ready yet. This would add a whole new layer of conflict to the story, not just between Naruto and his sister, but also with the village's expectations of Naruto as a ninja.
One aspect of a 'Naruto: Overprotective Kushina' fanfiction could be exploring Kushina's overprotectiveness in Naruto's early life. Maybe she's constantly hovering, fearing for his safety due to her own past traumas. This could lead to some interesting character dynamics, like Naruto feeling smothered at times but also understanding her love.
In fanfiction, Naruto and Minato often represent a connection between generations. Minato was a great ninja in his time, and Naruto is following in his footsteps. Fanfictions can explore how Naruto lives up to his father's reputation.
I'm not sure if there is such a specific fanfiction. Fanfiction can cover a wide variety of themes and scenarios, some of which might be rather strange or controversial. However, Naruto fanfiction often explores different relationships and alternate storylines, but this particular one seems a bit unorthodox and I haven't personally come across it.