Kushina could be an important character even though she's dead in the original story. In this fanfic, her spirit or memories could play a role in Naruto's upbringing. For example, Minato could tell Naruto stories about Kushina's feisty personality and her love for the village.
One possible plot could be Minato teaching Naruto and Sasuke his signature jutsu, like the Rasengan. He'd pass on his skills and wisdom, guiding them to be stronger and more responsible ninjas. Naruto might learn about his father's past more directly from Minato, and Sasuke could gain a new perspective on family and loyalty through Minato's influence.
Minato's presence would likely make them closer. He'd encourage them to see each other as brothers. Since Minato is Naruto's father, Naruto would have more confidence and be more at ease, which would make Sasuke respect him more. They'd have a common figure to look up to and follow his teachings together.
One possible plotline could be Minato teaching Naruto special jutsu early on. Since Minato was a very powerful ninja, he could pass on his knowledge of the Flying Thunder God Technique to Naruto at a young age, which would make Naruto even more formidable in battles against early foes.
Naruto would be more confident earlier. With Minato around, he wouldn't have to face the same level of loneliness and ostracism. So, he'd be more outgoing and less likely to act out for attention. He'd also have better control of his powers from the start, as Minato could train him properly. His fighting style would be more refined, combining Minato's speed and strategic thinking with his own natural abilities.
Minato, being a prodigy, would use his own knowledge of sealing techniques to help Naruto better understand the bond with the Nine - Tails. Kushina, on the other hand, would use her own experiences as a Jinchuriki. They would create a safe environment for Naruto to explore and learn about his power. They might also have him practice meditation to get in touch with the Nine - Tails' chakra in a calm and controlled manner.
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.
One of the main similarities is their self - sacrifice. Minato sacrificed himself to save the village and his son. Naruto has also shown that he is willing to put himself in harm's way for the greater good. He's always the first to jump into a dangerous situation if it means protecting those he loves. Another aspect is their leadership qualities. Minato was a great leader as Hokage, and Naruto has developed into a great leader as well, inspiring those around him.