Minato would likely be devastated. He sacrificed his life for Naruto, hoping for a great future for his son. Seeing Naruto die would shatter his hopes and dreams. He might first be in denial, unable to believe what he's seeing. Then, his grief could turn to anger, either at the situation or at those he believes are responsible. It's a tragic scenario that would change Minato's afterlife perception and his sense of purpose, which was always tied to Naruto's well - being.
The aftermath could be Minato's quest for revenge if Naruto's death was caused by someone. He would use his skills and knowledge to track down those responsible. Or, he could be plunged into a deep depression. He might isolate himself from the other spirits or entities in the afterlife. His whole existence could become centered around his grief and his memories of Naruto.
Well, first of all, Minato would likely be shocked. Naruto's past was full of hardships and loneliness. Minato would probably experience a mix of emotions. He might be sad that Naruto had to endure so much pain. He could also be proud of how Naruto overcame all those difficulties and still managed to grow into a strong and kind - hearted person. He might even try to find ways to comfort Naruto in this fanfiction world, like giving him some long - lost family memories or advice that could have made his journey easier.
One possible plot development could be that Minato uses the knowledge of Naruto's past to help him train better. Maybe he reveals some hidden family jutsu or techniques that Naruto can use to become even stronger.
Perhaps there was a curse or a disease that he couldn't overcome. In some fanfictions, they like to introduce unique and deadly diseases that not even the best medical ninja can cure. It could also be due to a failed mission where he was caught in a trap that was impossible to escape from, leading to his death.
It might be Iruka - sensei. Iruka was one of the first people to recognize Naruto for who he was and give him a sense of belonging. If Iruka were to die, Naruto would remember all those early days of support and kindness. His death would break Naruto's heart as it would be like losing a part of his family, the family that accepted him when no one else did.
One possible plot could be that Naruto witnesses the death of a fellow ninja from his village during a battle. Maybe it's someone he has trained with or has a friendly rivalry. This would cause him to cry as he feels a deep sense of loss for his comrade and also blames himself for not being able to protect them.
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 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.
I'm not sure specifically which fanfic this refers to. There could be various interpretations. Maybe it's a very dark and emotional take where Minato, Naruto's father, is somehow in a situation to witness Naruto's death, perhaps in an alternate universe where things go horribly wrong and the normal protection Naruto has is stripped away.