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.
There's also 'Overprotective Ruby' which focuses on Ruby being overly protective of her sister or friends. It has some really interesting scenarios where Ruby's protectiveness gets her into both comical and tense situations. This fanfiction does a great job of exploring Ruby's character in this context.
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 possible fanfiction could be where Ruby is overprotective of her team during a dangerous mission. Maybe she constantly checks on their safety, making sure they don't take unnecessary risks. For example, when they are facing Grimm, she might be extra vigilant about any threats towards Weiss, Blake, and Yang, and jump in to protect them even before they realize the danger.
She could also be shown as having a strong sense of worry. Maybe she has nightmares about her partner getting seriously injured in a Grimm attack and then becomes even more overprotective in the real world. She might start to limit his activities outside of the safety of their base or team.
One common trope is the overprotective girlfriend being overly cautious about her partner's battles. For example, she might try to keep him from taking on dangerous missions in the RWBY universe. Another is her getting jealous easily when others get too close to her partner during team interactions.
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.
Another common theme might be the contrast between Ruby's overprotective side and her normal, more carefree self. In the fanfiction, the author could play with this contrast, showing how Ruby is usually a positive and enthusiastic person, but when it comes to the safety of her team, she becomes a completely different, more intense person. This can add depth to her character and also create interesting storylines within the fanfiction.