Perhaps in this fanfiction, Naruto's family leaves him because they fear his godlike abilities. Naruto then has to prove that he can use his powers for good. He could start by helping the villagers who once shunned him. This would lead to a series of events where he gradually gains the respect and understanding of those around him, despite his family's absence.
One possible plot could be Naruto's journey of self - discovery as he tries to come to terms with being left behind. He might find hidden strengths within himself. Another could be him forming unexpected alliances with other characters who also have a sense of being alone. For example, he could team up with a wandering ninja who has his own story of abandonment.
A new character could be an old friend of Naruto's parents who shows up. They might have some information about his family and why he was left behind. Maybe there's a healer who tries to help Naruto deal with the emotional scars of being left behind. This healer could have their own backstory related to loss and abandonment as well.
It could be a powerful ninja from another village who sees Naruto's godlike powers as a threat to his own plans of domination. Since Naruto is already feeling vulnerable due to his family leaving him, this antagonist might try to take advantage of his emotional state.
Iruka could step in. He has always been like a mentor and a father figure to Naruto. He was the first one to really see Naruto's potential and give him the recognition he deserved. So in the absence of his family, Iruka would be a likely candidate to fill that family - like role.
As he grows up, Naruto could become very angry. He might develop a sense of abandonment and this could fuel his determination to become stronger. He would want to prove himself to his mother, wherever she is. In this fanfiction, his anger could be a driving force in his character development.
Well, it makes him more independent. Since he's left behind, he has to learn to fend for himself. He becomes more self - reliant and determined to prove his worth, not just to his family but to the whole village. He's constantly seeking validation and that drives him to train harder and grow stronger.
It could be a jealous fellow trainee. This person might spread false rumors about Naruto, which leads to him being left behind in training. The jealous trainee doesn't want Naruto to get stronger and be more popular.
Maybe Naruto is left behind in training because the instructor misjudges his abilities. As a result, Naruto starts training with a retired ninja who teaches him some old - fashioned but effective techniques. This gives him an edge when he finally rejoins his group.
Well, it might be about Naruto growing up without Kushina's presence. Maybe he has to face challenges alone and discovers things about his mother in the process.