Well, in such a fanfic, Naruto could be the son of someone like Jiraiya. Jiraiya was very close to Naruto and taught him a great deal. He might have had a secret relationship that led to Naruto's birth. Another possibility could be that Naruto is the son of an unknown shinobi from a far - off village who somehow ended up in Konoha.
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.
Well, Minato might constantly be by Naruto's side in the fanfiction. He could prevent Naruto from taking on any dangerous missions, even if Naruto is capable. For example, he may interfere when Naruto tries to join a risky battle against a powerful enemy, saying it's too dangerous for him.
One reason could be guilt. Since Minato wasn't there for Naruto when he was growing up in the original story, in the fanfiction, he might be overcompensating for that lost time. He feels like he has to make up for all those years he wasn't around to protect his son.
If Minato and Mei were Naruto's parents in a fanfiction, the story would take a whole new turn. In the original, Naruto was an outcast because of the Nine - Tailed Fox sealed within him. But with Mei as his mother, there could be different reactions from the village. Also, Naruto's training would be different. He might learn from Mei's combat style which is more aggressive and fluid compared to what he learned in the original. And the mystery surrounding his parents would be completely different. Instead of just the legacy of Minato, there would be the added mystery of Mei's influence and her village's secrets that could be passed on to Naruto.
Naruto could inherit Minato's calm and intelligent nature. Minato was known for his quick thinking in battle. From Mei, he might get her boldness. Mei was never afraid to speak her mind and take risks. So Naruto could be a combination of being smart in combat situations like Minato and fearless like Mei.
Minato's presence can have a huge impact. He can act as a mentor, teaching Naruto things he never knew about his family and heritage. His wisdom and skills can inspire Naruto to reach new heights in his training and ninja development.
He could feel it through a shared chakra link. Since they are related and Minato sealed the Nine - Tails in Naruto, there might be a latent connection that gets activated in the fanfiction, allowing him to sense Naruto's pain on a physical and emotional level.
Emotionally, Naruto would become more confident and stable. Having his father back would fill a void in his heart. This new - found emotional strength could translate into better chakra control and more powerful jutsu. Minato could also guide Naruto in handling the power of the Nine - Tails more effectively.