When it comes to his romantic relationship, if he time travels, it could be really interesting. If he goes back to a time before he met his partner, he might end up changing the way they meet or fall in love. Or if he travels forward in time, he could see how his relationship has developed over the years and make changes to ensure its longevity. His relationships with his subordinates might also change. They could view him differently, either with more respect because of his future knowledge or with some suspicion as his actions might seem out of place.
His relationship with his friends could change significantly. For example, if he travels back to a time when they were younger, he might be more protective of them. He could also inspire them in different ways, leading to stronger bonds. His relationship with his sensei might also be affected. He might be able to offer new insights based on his future experiences.
Minato's time travel can have a profound impact on his family relationships too. If he travels back to a time when his son Naruto was a baby, he could be more involved in Naruto's early life, which would change the dynamic between them. He could also go back to a time when his own parents were alive and form a different kind of relationship with them, learning things about his family history that he didn't know before, and this new knowledge could in turn affect how he relates to his family in his original time.