In a fanfiction, Naruto could be training in a secluded area and Yandere Koneko stumbles upon him. She immediately falls for his spunk and the fact that he doesn't give up easily. Yandere Koneko then tries to insert herself into Naruto's life by bringing him food and small gifts. Naruto is initially confused but then realizes she has a rather extreme way of showing affection and has to gently set boundaries.
A relationship could develop in a rather complex way. Yandere Koneko might first see Naruto as a target of her affection. She would do everything to get his attention, like sabotaging his meetings with other friends. Naruto, being the kind - hearted person he is, would initially think she's just a bit over - enthusiastic. But as her actions become more extreme, he realizes the seriousness of the situation. He could then try to help her overcome her yandere nature while also developing some sort of bond with her.
One idea could be that Naruto somehow gets trapped in a dimension where Kaguya has become a yandere for him. She tries to keep him there all to herself, while Naruto has to figure out a way to escape and also deal with her obsessive behavior.
A more complex fanfiction could involve Yandere Chan being a part of an experiment by Orochimaru. He combines some of her yandere traits with ninja abilities. She then targets Naruto, believing he has some special power that she needs. Naruto has to not only deal with her attacks but also try to understand her motives and perhaps find a way to reverse Orochimaru's experiment on her.
One idea could be a time - travel fanfic where Naruto and Koneko are sent back in time. They have to adapt to the different ways of the past while also trying to find a way back to their own time. This would give them the chance to meet younger versions of their friends and family, and perhaps change the course of history in small but significant ways.
One challenge could be the difference in their powers. Naruto has his ninja powers while Koneko has her own unique abilities. They might have trouble coordinating in battles at first.
One idea could be a crossover where Naruto somehow ends up in the world of Koneko. He could meet Koneko and they team up to face a common enemy. Maybe an evil force that is threatening both their worlds.
One idea could be that Sakura's yandere tendencies lead her to try and isolate Naruto from his other friends. She might start by spreading rumors about them to Naruto, causing some initial confusion and rifts in his relationships.
One idea could be that Tenten becomes yandere for Naruto after he saves her life in a battle. She then starts to secretly eliminate any girl she sees as a threat to her 'relationship' with Naruto. For example, she might try to sabotage Hinata's attempts to talk to Naruto.
Friendship is a very common theme. Since Naruto is known for his ability to make friends and Koneko has her own set of relationships, in fanfiction, they often form a strong bond of friendship that overcomes various obstacles.
Yes, there might be such a fanfiction out there. The Naruto and High School DxD universes are often mashed up in fanfiction, and creating a family bond like Naruto being Koneko's brother is an interesting concept that some writers might explore.