One common theme is the struggle of single parenting. Naruto has to handle all the responsibilities of raising a child alone, like providing for them, protecting them, and teaching them right from wrong. Another theme is the clash of different worlds. Since it's a crossover, there are elements from different anime universes that Naruto has to deal with while raising his child.
There's also 'Naruto: Single Father in a Fantasy Crossover'. This story focuses on Naruto raising his child in a world full of magic and different races from other animes. He struggles to fit in at first but then uses his determination and the values he learned in the Naruto world to build a good life for his family. It has a great plot that keeps you hooked.
One common theme is the struggle of balancing ninja duties and fatherhood. Naruto has to be out there protecting the village but also be there for his child.
One possible storyline could be Naruto struggling to balance his ninja duties with raising his child alone. Maybe he has to take the kid on missions sometimes, teaching the little one about the ninja world along the way. Another could be Naruto dealing with the judgment of the village as a single father, showing how he overcomes that and still raises a strong and kind - hearted child.
There might be a fanfiction where Naruto becomes a single father because of some unforeseen circumstances during a mission. He then has to teach his child the ways of the ninja world while dealing with his own emotional turmoil. This could explore how Naruto's past experiences shape his parenting style.
In some 'naruto is a father crossover fanfiction', there could be a storyline where Naruto is a father in a crossover with the Harry Potter world. His child could be a student at Hogwarts, and Naruto, with his experience of being a hero, tries to understand the magic world and protect his child from the dark forces. Maybe he uses his chakra in unique ways within the magical environment.
In a crossover with the Attack on Titan world, characters like Eren could interact with Naruto. Eren, with his strong will to fight for freedom, could learn from Naruto's experience as a father and a hero. Levi might also be interested in Naruto's combat skills and how he trains his child in the ways of the ninja.
In single father fanfiction, Naruto's character often develops a new level of patience. He has to deal with his child's tantrums and needs, which is different from his ninja battles. This makes him more empathetic.
One possibility is that a writer might create a backstory where Naruto's unique chakra or abilities are needed to save Kunou's mother from a great danger. In the process, a bond forms between them and through some unorthodox means, Naruto becomes the father. Another aspect could be that in the fanfiction world, there are new rules and the author wants to explore the combination of Naruto's ninja world elements with the devil - based world of 'Highschool DxD' to make Naruto Kunou's father.
He would become more empathetic. As a single father, Naruto would have to understand his child's feelings more deeply. He'd be quicker to pick up on when the child is sad or happy, and adjust his parenting accordingly. For example, if his child is sad about not having a mother, Naruto would have to be extra sensitive.