At first, Naruto would likely be extremely confused. He would try to find reasons for Kushina's actions. He might start to question his own worth, thinking that he has done something wrong. As time passes, he could become angry. Angry at Kushina for leaving him and at his sister for seemingly taking his mother away. This anger could fuel his determination to prove himself and show Kushina that she made a mistake.
Naruto might initially be in shock. He has always counted on Kushina's love, and this sudden abandonment would be a huge blow. He could become withdrawn and quiet, not understanding why his mother would do such a thing.
One possible reason could be some sort of dark influence or curse that makes her lose her maternal instincts. Maybe a powerful enemy targets her and in order to protect Naruto from further danger related to her, she feels forced to abandon him. Another reason might be that she is made to believe false information about Naruto, such as that he will bring great disaster to the village in the future.
At first, Naruto is likely to be heartbroken. Konoha has been his home, and he has always longed for acceptance from the villagers. So being abandoned would be a huge blow to him.
Naruto would be devastated. He sees Kakashi as a mentor and father figure. He might initially go into denial, not believing that Kakashi would actually abandon him.
In the fanfiction, it could be that Kushina is pressured by external forces. For example, there might be a powerful group or individual who forces her to abandon Naruto for his sister. This could be part of a larger political or power - play scheme. Also, it's possible that Kushina has a moment of extreme emotional confusion. She might see something in Naruto's sister that she once desired for herself when she was younger, and in a moment of weakness, she decides to focus on the sister instead of Naruto.
He could become very determined to find out why Sakura left and try to win her back. Naruto is known for his perseverance, and he wouldn't give up easily on his family. He might also start to question his own actions and wonder if he could have done something differently to prevent this.
He may develop trust issues. Being abandoned by his mother could make him more cautious about getting close to people. However, this could also make him more determined to prove himself. He might strive to be the best ninja in the village to show that he is worthy of love and acceptance, despite being abandoned. For example, he could push himself extra hard during training.
In such a fanfiction scenario, the village of Konoha would be affected too. Minato is a respected figure. His abandonment could cause a scandal. Naruto might not have the same level of protection from the village elders. This could lead to different power dynamics within the village. Maybe other ninja clans would try to take advantage of Naruto's situation. Also, Kushina's family might react in various ways, some might try to find Minato and some might focus on taking care of Kushina and Naruto.
Naruto might be extremely heartbroken. He has always looked up to his mother, and being disowned by her would be a huge blow. He could become withdrawn and start to question his own worth.
Kushina would be extremely worried. She would rush to Naruto's side immediately and start using her medical knowledge or any available resources to help him get better.
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.