In such a fanfiction, Naruto might finally get the father - son relationship he always craved. Minato could train Naruto personally, passing on his powerful jutsu and wisdom. Naruto would grow up with a strong sense of family and might become an even more confident ninja at a younger age.
One possibility is that with Minato around, Naruto would be exposed to different political and ninja - related matters much earlier. Minato could guide him on how to handle the complex relationships within the Hidden Leaf Village. They might also go on adventures together, and Naruto would learn combat skills and strategies directly from his father. This would make Naruto a more well - rounded and perhaps less impulsive ninja as he would have his father's guidance from the start.