His relationship with Sasuke would likely be very different. Without the shared experiences in Konoha, their initial rivalry might not be as intense. Naruto might not be as desperate to bring Sasuke back. And his relationships with his other Konoha friends like Sakura and Kakashi would also change. He'd be more connected to Yugito's friends and allies instead.
Naruto's character would likely be more calm and collected. Yugito Nii's influence might make him think before he acts. He would still be determined but in a more refined way.
One possible plot could be that Naruto grows up with Yugito Nii's unique teachings. He might learn different jutsu styles from her. For example, he could master some of the Nii clan's secret techniques. Yugito Nii could also instill in Naruto a different set of values compared to what he would have learned in Konoha on his own. This could lead to Naruto having a more nuanced view of the ninja world and different relationships with the other villages.
Naruto's training would involve a deeper understanding of tailed beasts from an early age. Since Yugito is a jinchuriki, she could share her experiences and knowledge about the Nibi with Naruto. This would give him an edge when it comes to dealing with Kurama. He might learn how to better communicate with Kurama or even gain some new abilities related to the tailed beasts' chakra earlier than in the original story.
In this fanfiction, the story might focus on how Naruto's character develops under Yugito's influence. Yugito could introduce Naruto to a different side of the ninja culture that he may not have been exposed to otherwise. For example, she might have connections to certain clans or traditions that Naruto becomes a part of. This could lead to new friendships and alliances for Naruto, as well as new enemies who might not like this new 'Naruto' that is being shaped by Yugito. Also, Naruto might learn different stealth techniques from Yugito, as she is from a different village and has her own set of skills in that area.
His relationship with Sasuke would be different. Instead of the intense rivalry based on power and recognition, it could be more about their different approaches to protecting the village. Naruto, with his skills from Totosai, might offer Sasuke unique weapons or tools to aid him in his missions.
If Naruto was raised in a Jinchuriki Sanctuary in fanfiction, his relationships would undergo a significant transformation. First of all, he would have a group of peers who are also Jinchurikis. This would create a sense of camaraderie that is based on a mutual understanding of the unique challenges they face. His relationships would not be marred by the fear and prejudice that he faced in Konoha. Instead, they would be built on mutual respect and the common goal of mastering their Jinchuriki powers. He might form closer bonds with some Jinchurikis who could become like family to him. And in terms of romantic relationships, he could potentially find a partner who not only accepts him but also shares his powerful and complex identity as a Jinchuriki.
He'd probably be more cautious. Quarians live in a fragile environment, and Naruto would grow up learning to be careful. So, instead of his usual head - on approach, he might think more before acting.
Naruto might also feel a sense of responsibility. He might think that he did something to cause Yugito to act this way. So he could start to limit his own actions to avoid triggering her yandere behavior. For instance, he might stop being so friendly with other girls in front of her. But at the same time, he would not give up his own dreams and values, and would try to make Yugito understand that her behavior is not acceptable in a way that is both firm and kind.
Their relationship could start as comrades in misfortune. As they face the hardships of being banished, they rely on each other more and more, gradually developing a deep bond of friendship. Over time, this could turn into a romantic relationship as they realize how much they mean to each other.
Their relationship would transform into a true partnership. Naruto, who has always been about protecting the village and his friends, would now have a new focus on protecting his family. Yugito, on the other hand, would rely on Naruto more for emotional support during the pregnancy and after the baby is born. They would share the joys of seeing the baby's first steps, first words, etc. Their relationship would be centered around the well - being of their child, and they would do whatever it takes to ensure the baby has a happy and safe life.