Yes, there are likely some 'Naruto Son of Evil Minato' fanfictions out there. Fanfiction websites are full of various creative takes on the Naruto universe. You can start by checking popular fanfiction platforms like FanFiction.net or Archive of Our Own. Just search for the specific title or relevant keywords to find ones that match this concept.
Well, in some fanfictions, it could be a result of a powerful jutsu gone wrong that sends Naruto back in time, allowing him to have a son named Minato in an alternate timeline. This creates a whole new set of dynamics as Naruto now has to deal with the fact that his son is named after his father, and he also has to navigate the politics and relationships of the past world while trying to ensure a better future for his new family.
Sakura could be a significant character. In the context of Naruto being Minato's son, her relationship with Naruto might change. She could be more in awe of him at first or have different expectations. Also, Sasuke is likely to be a main character. His rivalry with Naruto could take on new dimensions as Naruto has the added legacy of being Minato's son. Their battles and interactions might be more intense and influenced by Naruto's heritage.
The relationship can be developed by having Minato appear in Naruto's memories more vividly. For example, Naruto could start having flashbacks of Minato's training sessions or family moments that he didn't know about before. This would make Naruto feel closer to his father.
One possible fanfiction could be about Kagome somehow traveling to the Naruto universe. Maybe she meets Minato and they form an alliance. And she discovers that Naruto is Minato's son. Shippo could be a unique addition, perhaps he has some special abilities that are useful in the Naruto world.
Some fanfictions focus on Naruto's relationship with the village. As Minato's son, the villagers' perception of him could be different. They might have higher expectations from the start. This could lead to Naruto either struggling more with the pressure or using it as motivation to prove himself even faster. There could also be stories about Naruto uncovering secrets about his father that were hidden from him in the original story.
Well, perhaps the plot could involve Minato having a secret evil plan all along. He could have used Naruto as part of this plan without Naruto knowing. Naruto then starts to notice strange things related to his father. As he digs deeper, he finds out about Minato's true nature. This could lead to Naruto having to choose between following in his father's footsteps (for some strange reason like power) or defying him and becoming a true hero on his own terms. The story could also involve Naruto's friends either turning against him because of his relation to Minato or helping him to overcome this difficult situation.
Well, the story could develop in many ways. Maybe Naruto could be an orphan found by someone else in the village, like an old ninja who decides to train him in secret. This would change Naruto's backstory completely. He might not have the same kind of pressure or expectations that come with being the son of a famous Hokage. His character could grow in a different direction, perhaps being more independent from the start as he has to create his own identity without the shadow of his 'father' Minato.
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.