Perhaps Naruto discovers some hidden powers or abilities that Kunou has inherited from him, which leads to a whole new adventure. They might go on a journey to understand and control these powers together. Also, Naruto could face challenges from the village elders who are not so accepting of Kunou at first.
One possible antagonist could be some of the traditionalist shinobi in the village who oppose Naruto's new family situation. They might see Kunou as a threat due to her heritage.
In fanfiction, the idea of Naruto being Annabeth's father might start with a portal or time - travel element. For example, Naruto could be sent through a portal to the world of Annabeth. He might save her mother from a great danger, and in the process, they fall in love. Then, Annabeth is born. Another way could be that there is a curse or a prophecy that links their two very different worlds together, and Naruto is fated to be her father.
Another plot development could be that with Sarutobi as his adoptive father, Naruto has access to different mentors. Sarutobi could call in favors from other great ninjas to train Naruto. This would expose Naruto to a wider variety of fighting styles and strategies. Maybe he gets trained by Kakashi earlier, or even has the chance to learn from some of the retired or older ninjas who usually keep to themselves.
Naruto himself might develop a more global and cultural understanding. He starts as a ninja from the Hidden Leaf but as he becomes the 'father of Asia', he has to learn about different Asian cultures, religions, and traditions. This could make him more diplomatic and patient.
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.
One possibility is that Naruto's friends launch a rescue mission. They would use their unique skills, like Sasuke's Sharingan or Sakura's medical ninjutsu combined with her combat skills, to find and save Naruto.
Well, one possible plot development could be Naruto training even harder to prove himself. After the Chunin Exams, he might seek out new jutsu or ways to improve his skills. Maybe he starts to focus on his control over the Nine - Tails' chakra more intensively.
One possible plot development could be that Naruto's friends in Konoha realize he's missing and start a search mission. They might suspect Kumo immediately due to the history of tensions between the two villages. Meanwhile, in Kumo, Naruto could be held in a secret location. Some in Kumo might want to use him as a bargaining chip against Konoha, while others might see his potential and try to turn him into an asset for Kumo.
In this fanfiction, Itachi might also train Naruto in the ways of the Sharingan. Even though Naruto doesn't have the Sharingan naturally, Itachi could find ways to make Naruto understand the principles behind it, like how to read an opponent's movements more accurately. This could lead to Naruto having an edge in battles against opponents who rely on speed and deception.
Perhaps the plot could involve some sort of magic or curse that is causing Naruto to be in this state. The story might then focus on how the Naruto world's medical ninjas try to figure out what's wrong. They could run all sorts of tests and experiments. And there could be a race against time as Naruto's condition worsens.