One idea could be that the daughter has to hide her identity in the village that banished Naruto. She might inherit some of Naruto's unique abilities like his shadow clones. She could use these abilities in secret to help the villagers without them knowing she's related to the banished Naruto.
One possible plot could be that Naruto, after being banished, discovers a new place where he starts his own family. He might meet a kind-hearted woman who accepts him for who he is. They could have a child together, and Naruto would be determined to protect his new family from any threats, including those who might still hold a grudge against him from his past in Konoha.
Well, in this fanfiction scenario, perhaps Naruto's daughter is born with some unique power that was passed down from Naruto's Uzumaki heritage. Naruto, being banished, is determined to keep her safe from the forces that might want to use or harm her. The story could follow their journey as they encounter various challenges and make new allies along the way. They might even form a small community of outcasts who support each other.
In the 'banished naruto has a family fanfiction', Naruto might be banished and end up on an island. There he meets a group of outcasts like himself. Among them, he finds a partner and they start a family. Their family grows up learning Naruto's ninja ways and they all strive to create a better life on the island, away from the politics and judgment of the ninja world that banished Naruto.
In a 'Naruto banished has a child' fanfiction, perhaps Naruto was banished unjustly. His child could be a source of hope for him. The story could involve Naruto passing on his dreams and values to the child. They might journey together to find a new place to call home, and along the way, the child discovers their own unique powers that are a combination of Naruto's and something new. Naruto would be a protective and loving father, determined to give his child a better life than he had.
In such a fanfiction, perhaps Naruto was banished due to false accusations or political intrigue. His son might grow up away from the Hidden Leaf, learning unique skills from Naruto. The son could have a strong sense of justice, wanting to clear his father's name. Maybe he discovers new forms of chakra or has special abilities that are a combination of Naruto's Uzumaki bloodline and the teachings from their exile.
Naruto would become more cautious. He has a child to protect now, so he can't be as reckless as he used to be. He'd be more of a planner, thinking about the future and how his actions will affect his child.
Well, one possibility is that Naruto's son would grow up without the recognition of the village. Naruto might teach his son all the skills he learned, like shadow clones, on their own. And they could form a small family unit away from the village, living a simple but peaceful life.
Perhaps his family consists of a group of fellow banished ninjas who become his surrogate family. There could be a strong - willed female ninja who becomes his partner, and together they have a child. And also an old sage - like figure who acts as the family's wise elder, guiding them through the difficulties of living in exile.