Another idea is a story where Sasuke and Minato are on a joint mission in an alternate dimension. They have to rely on each other's skills to survive. Minato's speed and strategic thinking combined with Sasuke's Sharingan abilities would make for an exciting adventure. Along the way, they could learn more about each other's personalities and develop a mutual respect.
In a fanfiction, an overprotective Minato would be like a storm cloud over Sasuke and Naruto's relationship. Minato's actions, driven by his concern for Naruto, would constantly disrupt the natural development of Sasuke and Naruto's friendship. Sasuke would see Minato as an obstacle to his connection with Naruto. Naruto, while loving Minato, would also feel caged by his overprotectiveness. This could lead to a downward spiral in their relationship if not resolved. But if they all sit down and talk things through, it could transform into a more positive and understanding dynamic.
There are many great Sasuke and Minato fanfictions out there that are family - friendly. You can start by looking on fanfiction.net. Search for their names in the Naruto section and then filter through the stories by reading the summaries. Some of them might focus on their mentor - mentee relationship in a non - romantic way, like how Minato's skills or values could influence Sasuke's growth in an AU (alternate universe).
Minato would likely be extremely shocked. Naruto is his son, and the idea of Naruto attacking him would be completely unexpected. He would probably try to talk to Naruto first, to find out what is wrong and why he is being attacked.
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.
On a more personal level, they could face internal guilt. As Naruto grows up and achieves great things on his own despite their neglect, Minato and Kushina may realize what they've missed out on. This realization could cause them a great deal of internal turmoil and regret for not being there for their son when he needed them.
In some fanfictions, Minato saves Naruto physically. For example, he might use his teleportation jutsu to appear right in the middle of a fight and whisk Naruto away from danger. In others, he could save Naruto spiritually. He might enter Naruto's mind, like in the fanfic 'Minato's Mind - Saving Mission', and give him the strength and confidence to overcome his inner demons. Sometimes, Minato saves Naruto from a political situation. For instance, in 'Minato and the Hidden Leaf's Politics', he uses his influence and wisdom to protect Naruto from being used as a political pawn.
Yes, there are likely some 'Harry is Minato' fanfictions out there. Fanfiction platforms have a wide variety of crossovers. You can try searching on popular fanfic sites like Archive of Our Own or FanFiction.net.
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.