Yes, in fanfiction, Naruto can do all sorts of things that might not be shown in the original series, like rapping. Writers often take creative liberties in fanfiction to explore different aspects of characters. So it's not unusual to find a story where Naruto has a hidden talent for rapping, perhaps to inspire his friends or as a new form of ninja art.
One possible motive could be that Minato is under some sort of dark magic or mind control. In fanfiction, authors often play with the idea of characters being forced to act against their true nature. So, if Minato is being controlled, he might end up doing something as extreme as killing Naruto.
Many fanfictions show their relationship as one of mutual respect and admiration. Minato is often portrayed as being attracted to Kushina's strong will and red - hot hair, which is a symbol of her fiery personality. They start as friends, training together and gradually realizing their feelings for each other.
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.
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.
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.
One element is the lyrics. If the lyrics are about dark topics like death, ghosts, or curses, it can be scary. For example, lyrics that describe a spooky encounter with a supernatural being. Another is the tone of the rap. A slow, deep, and menacing tone can add to the scariness. Also, the setting where the rap takes place. If it's in an abandoned place like an old factory or a haunted house, it gives a creepy vibe.
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.
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.