One reason could be that she lost so much time with Naruto due to her early death in the original story. So in the fanfiction, she's overcompensating for that lost time by being possessive.
In the fanfiction, Kushina's possessiveness could be manifested in various ways. She might be very controlling of Naruto's daily activities. For instance, she would decide what he eats, when he sleeps, and how he spends his free time. Also, if there are any female characters showing interest in Naruto, Kushina would be quick to step in and make it clear that Naruto is 'hers' in a sense. This could create some interesting conflicts in the story, as Naruto might feel suffocated by her over - protectiveness at times, while also understanding that it comes from her love for him.
One plot idea could be Kushina being overly possessive when Naruto starts making new friends in the village. She might be constantly worried about his safety and try to limit his interactions in a motherly yet overbearing way. For example, she could be hesitant when Naruto wants to go on missions with his friends at first.
Kushina's possessiveness could initially slow Naruto's growth. If she's too overprotective, he might not get the full experience of taking risks and learning from his mistakes. For instance, she might prevent him from going on dangerous missions early on.
Another aspect could be that the fanfiction delves into how Kushina's presence affects Naruto's relationships with others. For instance, his relationship with Sasuke could be different. With a strong maternal figure in his life, Naruto might be more stable emotionally and be able to approach Sasuke in a more understanding way, which could potentially change the whole dynamic of their rivalry and friendship.
In some Naruto fanfictions, Gaia might be possessive of Naruto because he represents a new hope or a different way of doing things. Gaia, being an important entity in the fanfiction universe, might see Naruto as a way to change the status quo. His kind - hearted nature and strong will could be what attracts her, and she's possessive to protect and guide him so that he can fulfill the potential she sees in him. She might also be possessive because she's the only one who truly understands his significance in the grand scheme of the fanfiction world.
In some fanfictions, the authors might take creative liberties and create alternate universes where Naruto and Kushina interact in different scenarios. For example, they could be on a joint mission together, and through that, we see their personalities shine. Kushina's fiery nature and Naruto's determination would make for an interesting dynamic.
One possible fanfiction could be about Kushina finding Naruto in a situation where he's lost in a forest. Maybe she uses her unique chakra sensing abilities to track him down. It could be a heartwarming story of a mother reuniting with her son.
In some fanfictions, Kakashi might be possessive of Naruto because he sees Naruto as a unique and important student. Naruto has a special energy and determination that Kakashi admires. He may also feel a sense of responsibility towards Naruto, as Naruto has no family, and Kakashi wants to protect him. This possessiveness could be his way of ensuring Naruto's safety and growth.
Well, in Naruto fanfiction, Anko might be possessive because she has a strong personality. She's a character who is confident and doesn't like to share what she considers hers. Maybe she has a special connection to Naruto in the fanfic world, like she sees his potential and wants to be the one guiding him, so she becomes possessive to keep others from interfering with that relationship.