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.
The Third Hokage might also play that role. He has always been watching over Naruto. He made sure Naruto had a place to stay and food to eat. He was a sort of protector for Naruto. In the context of Naruto being left behind by his family in fanfiction, the Third Hokage could step up more and be like a grandfather - like figure for Naruto, providing him with stability and guidance.
His father, Minato, could be a likely candidate in a really dark fanfiction. Maybe he was resurrected in an imperfect way and his mind was warped, causing him to turn on Naruto.
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.
His mother, Kushina, could also be part of the family that wants him back. She was a kind - hearted and strong - willed woman. If she were alive in the fanfiction, she would be desperate to have her son with her. She would want to protect Naruto and share all the things she didn't get to when he was growing up, like teaching him about their Uzumaki heritage.
He would most likely meet his parents, Minato and Kushina.
His father, Minato, could be one. Maybe there's some time - travel or alternate reality situation where Minato has been corrupted in some way and Naruto has to fight him to set things right.
He might try to prove himself. Naruto could focus on becoming stronger and more successful as a ninja. By showing his family that he can achieve great things and that he's a good person, he hopes to change their minds. For example, he might take on difficult missions and complete them with excellence.
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.
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.
Another reason might be related to family politics. In some complex family structures in the Naruto universe, there could be different factions. Naruto might be on the wrong side of the power struggle within the family. His views or actions could be seen as a threat to the traditional power structure of the family, so they hate him.
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.