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.
There are quite a few out there. In a lot of these 'Naruto overprotective sister fanfiction' stories, the sister is usually a new character created by the author. Her overprotective behavior can stem from Naruto's status as a jinchuriki or simply because she loves him dearly. For instance, she might train secretly to be strong enough to protect him. These fanfictions can offer a different perspective on Naruto's growth and the relationships he forms within the Naruto universe.
It's appealing because it adds a new family - related angle. Naruto didn't really have a strong family presence in the original, so having an overprotective sister fills that gap.
The plot could start with Naruto's sister being introduced suddenly. Maybe she was away for a long time, and now she's back and realizes how much Naruto has grown up but also how much danger he's in as a ninja. She then starts to follow him around everywhere, much to Naruto's annoyance. For instance, she might show up during his battles and try to jump in to protect him even when he doesn't need it.
One interesting fanfic could be 'Naruto's Protective Sister: Konoha's Guardian'. In this fic, the sister uses her unique jutsu skills to protect Naruto from various threats. Another might be 'Sisterly Love for Naruto' where she constantly fends off those who might harm Naruto due to his jinchuriki status.
Often, in fanfiction, you'll see Naruto being overprotective when his sister is about to go on a mission. He'll try to convince her not to go, or if she does, he'll insist on going with her. He might also be overly cautious when she's interacting with new people or in new environments. For example, at a village festival, he'll keep a close eye on her to make sure no one takes advantage of her. And if she gets injured, even slightly, Naruto will go into full - on protective mode and might even overreact a bit.
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 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.
One common theme is loyalty. The overprotective sister is often extremely loyal to her sibling, willing to go to great lengths to keep them safe. For example, she might put herself in danger without hesitation.
Well, it could make other characters a bit wary of approaching his sister. For example, if Naruto is overly protective, some characters might think twice before getting too close to his sister in case they anger Naruto. It could also lead to some misunderstandings. Maybe some characters misinterpret Naruto's protectiveness as his sister being weak or in need of constant supervision, when in fact she might be quite capable on her own.