I'm not sure if there is such a fanfiction specifically. Fanfiction websites have a vast range of works, but 'lemon' fanfictions often contain inappropriate content. It's better to focus on non - explicit fanfictions that explore the relationships and stories in a more positive and appropriate way.
One idea could be that as Minato is dying, he passes on his special jutsu knowledge to Naruto in a final moment of father - son connection. Kushina, on the other hand, tries to comfort Naruto while also mourning Minato.
One possible reason could be a misunderstanding. Maybe Minato thought Kushina had done something to endanger Naruto when in fact she hadn't. In the heat of the moment, he lost his temper and slapped her.
In a fanfiction, if Minato were to slap Kushina, it would be a huge shock to the Naruto - Kushina relationship. It could potentially cause a rift between Naruto and his father Minato in Naruto's mind. Also, Kushina would likely be deeply hurt and angry, which might lead to her distancing herself from Minato. This event could also change the way Naruto views his family's past and his parents' relationship.
In the fanfiction, it could be that a powerful enemy uses a forbidden jutsu that merges Naruto's consciousness with that of a world where Minato is female and Kushina is still alive. Naruto has to adapt to this new reality and figure out how to work with them to break the jutsu. During this time, he discovers new aspects of his parents' personalities. Female Minato might be more nurturing yet still have the strategic mind of his father, and Kushina could be even more protective. They form a strong bond as they fight to return Naruto to his own world.
If Minato didn't die in the fanfiction, he could have been a great mentor to Naruto. He could have taught Naruto advanced ninjutsu much earlier, and Naruto might have become even more powerful at a younger age.
One possible aspect to analyze in a Kushina x Minato fanfic could be their relationship dynamics. Their love was strong and Minato was always very protective of Kushina. Fanfics might explore their courtship in more detail, like how they first fell for each other.
A common theme could be the exploration of their relationships. For example, how Minato balances his love for Kushina and his role as a father to Naruko. There could also be a theme of legacy. Minato is a great Hokage, and Naruko could be on a path to follow in his footsteps while being influenced by Kushina's strength. Also, friendship could be a theme, as they support each other through tough times in the village.
At first, Naruto might be really confused by the presence of a female Minato. But as they start training together, he'd see her skills and start to respect her in the same way he did his father. With Kushina, he'd feel an instant connection as his mother. As time goes on, they'd become like a family unit, with Naruto seeing female Minato as a new version of his father and having a closer relationship with Kushina than he ever did in his own time since she's alive in this fanfiction.
Yes, there are likely fanfictions out there that focus on the relationship between Naruto, Mikoto, and Kushina in a non - lemon way. You can start by looking on major fanfiction platforms like Fanfiction.net or Archive of Our Own. Search for the characters' names and filter through the results to find stories that suit your taste.