He might go into hiding for a while and train intensively. He could come out with new and improved skills that shock everyone. For example, he could master a new form of Rasengan that is even more powerful. Then he might start to build an underground network of ninjas who believe in his cause and are against the unjust banishment.
In the fanfiction, after being banished, Naruto might cross paths with an ancient and powerful ninja. This ninja could take Naruto under his wing and teach him secrets that were lost to the modern ninja world. With this new knowledge, Naruto could start a revolution in the ninja world, changing the way villages are run and how ninjas are treated. His banishment would be the starting point of a much larger change.
Naruto might initially be shocked and feel betrayed. But he would soon gather his strength. He could use his skills to survive in the wild or in a new land. He would probably keep training to get even stronger.
One possible plot could be that Naruto, feeling betrayed by Konoha after banishment, decides to join Akatsuki. He might initially be an outcast even within the Akatsuki, but gradually gains their respect with his powerful jutsu. He could use his new position to try and change Akatsuki from within, aiming to stop the more extreme members from their plans of world destruction.
His relationship with Sasuke would become even more complex. Sasuke might see Naruto's joining of Akatsuki as a betrayal or a sign that Naruto has finally given up on Konoha. Naruto's old friends in Konoha, like Sakura and Kakashi, would be very confused and hurt. They might try to bring him back, but also be wary of his new Akatsuki ties. And within Akatsuki, Naruto would have to navigate relationships with members who have different motives and personalities, some of whom might not trust him at all.
Naruto could also be defiant. Given his strong - willed nature, he might not accept the banishment quietly. He may try to prove his innocence or the importance of his presence in the village. He could use his godlike powers to make a statement, not in a harmful way, but to show that banishing him is a mistake. For example, he might perform some great feats to protect the village from an outside threat even while banished, to show that he still cares about it.
Well, for one, Naruto would no longer be in Konoha to influence his friends directly. His friends like Sasuke and Sakura would have to develop without his constant presence. Sasuke, for example, might not have as strong a motivation to become stronger if Naruto wasn't there as a rival. The story could then shift focus to how Konoha copes without Naruto and the potential chaos or stability that follows. Also, Naruto would have to find his own path outside the village, which could lead to him making new allies or enemies.
On a larger scale, it could disrupt the balance of power in the village. Without Naruto, the village may be more vulnerable to external threats. This could lead to the other ninja having to step up and fill the void left by Naruto. It might also cause internal power struggles as different groups try to take advantage of the situation, either to gain more influence or to try and bring Naruto back for their own reasons.
His banishment might make him more open to joining a bloodline. Since he's been cast out, he has less to lose and is more likely to take risks. So, when the opportunity to join a bloodline comes up, he might jump at it without hesitation.
At first, Naruto might be extremely confused. He has always considered the village his home and Kushina as someone important. So being banished by her would leave him feeling lost and not understanding why it happened.
At first, Naruto would likely be very angry and hurt. He's always wanted to be accepted in his village, and banishment would feel like a huge rejection. But he's also a fighter. So, he'd probably channel that anger into getting stronger. He might have moments of self - doubt, but his determination would push him forward.
In the context of this fanfiction, Naruto's family might banish him because they don't fully understand his 'godlike' powers. They see the surface level of his new strength and assume the worst. Maybe they think he has been corrupted by some unknown force. Also, it could be related to power politics within the family. Some members might see Naruto's power as a threat to their own position and influence, and so they convince the rest of the family to banish him to safeguard their own interests.