There probably is. Fanfiction is a place where writers can reimagine relationships. If Kyuubi was Naruto's older brother, it could rewrite many aspects of Naruto's life. For example, Naruto might have had a different upbringing with Kyuubi around. And it could also affect how Naruto deals with his enemies, as he would have the power and guidance of his older brother Kyuubi. It's a really interesting concept that fanfic writers might explore.
One possible plot could be that Kyuubi protects Naruto from the very beginning. Instead of being seen as a monster, he's Naruto's brother and uses his power to shield Naruto from the villagers' hatred. Maybe they train together in secret, and Naruto becomes much stronger and more confident earlier in the story.
It could be full of action. Naruto would bring his ninja skills to Issei's world. He might train Issei in combat, much like he trained with Sasuke and others. Their relationship could also be full of brotherly banter and support.
It could entail Naruto having a very different upbringing. Since he's older, he might have to take on more responsibilities in the family. He could be the one to protect Minato from the early threats that Minato faced in the original story.
One possible plot could be Naruto protecting Serena from various threats in their world. Since Naruto is known for his determination and strength, he would use his ninja skills to keep Serena safe. Maybe they live in a world where both ninja and other magical elements exist, and Serena has some special power that makes her a target, and Naruto is constantly on guard.
One type of fanfiction could be where Kyuubi's obsession with Naruto is rooted in seeing Naruto as a symbol of change. Naruto, with his determination, might make Kyuubi, who has been trapped for so long, believe in a different future. In this kind of fanfiction, Kyuubi could constantly be trying to protect Naruto in his own way, even if Naruto doesn't fully understand it at first.
Well, it would be a really wild concept. Naruto's ninja world and Vegeta's Saiyan heritage are so different. Maybe Naruto would teach Vegeta some ninja skills like stealth and using chakra in unique ways. And Vegeta might introduce Naruto to Saiyan combat techniques. It could be a story full of clashes between their different values and powers, but also of them learning from each other.
It could work if there was a shared backstory created for them. Perhaps they both have a common ancestor or some ancient power that links them. Naruto's strong sense of loyalty and protection could be extended to Natsu as his younger brother. He could teach Natsu some of his ninja values like never giving up and the importance of teamwork. Natsu, in turn, could show Naruto the more carefree and adventurous side of the Fairy Tail world.
In this fanfiction, their relationship becomes more of a partnership. Instead of Naruto just using the Kyuubi's power, they work together as brothers. Naruto might start to understand the Kyuubi's feelings and motives better.
Yes, there are likely some fanfictions with this concept. Fanfiction writers often explore unique relationships and alternate storylines. They might create a scenario where Naruto is Sasuke's older brother to develop different character dynamics, explore new plotlines, and add their own creative twists to the Naruto universe.
There could be. Fanfiction writers like to explore different 'what - if' scenarios. Since Naruto and Kushina have a strong connection in the original series, some writers might be intrigued by the idea of reversing their relationship in a fictional context. But it goes against the established lore of the main Naruto storyline.