Yes, there are some fanfictions out there with this concept. Some fans like to explore unique family relationships in the Naruto universe through fanfiction.
In some fanfictions, authors might create an alternate universe where Naruto could be Minato's brother. However, in the original Naruto series, Minato is Naruto's father. Fanfiction allows for a lot of creative liberties, so it's possible to find such an interesting plot twist in some works.
Perhaps in this fanfiction, Naruto has to keep his identity a secret from Minato. He could be from an alternate future where things went wrong, and he's there to make sure Minato becomes Hokage and prevents certain disasters. So he has to subtly guide Minato without revealing who he really is.
The idea of Minato being Naruto's brother is appealing because Minato was such a powerful and respected ninja. It gives Naruto a different kind of support system from the start. In a fanfiction, it can explore how Naruto could have developed with Minato by his side, which is very different from his original lonely childhood.
One popular 'Naruto and Minato brother fanfiction' is 'The Bond Beyond Time'. It delves into how Minato's presence as an older brother could have influenced Naruto's growth. It shows Minato training Naruto from a young age and sharing his wisdom about the Uzumaki heritage.
Well, one possible plot could be that since Naruto is Minato's brother, he is not ostracized by the village. Instead, he is seen as a potential heir to Minato's legacy. This would change his entire character arc. He might not have the same drive to prove himself, but rather focus on living up to Minato's name. There could also be a plot where they face a common enemy together, and Naruto's bond with Minato helps him unlock new powers or techniques. Another aspect could be the exploration of their family secrets and how it impacts the whole Hidden Leaf Village.
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.
One popular theme is Minato getting to know Naruto in the afterlife. Since Minato died when Naruto was a baby, fanfictions often explore their relationship in a spiritual realm.
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.