There probably is. Fanfiction writers often come up with very creative and unexpected crossovers. However, the quality can vary greatly. Some might be really well - written with interesting plotlines that blend the Naruto and Inuyasha universes in a unique way considering the relationship you mentioned, while others might not be as good.
It could be really wild. Naruto's energetic and friendly nature would contrast with Sesshomaru's cold and aloof personality. Maybe there would be a story about how Naruto discovers his connection to Sesshomaru and has to navigate the Inuyasha world with his ninja skills.
Sesshomaru would likely be aloof and haughty at first. He might look down on Naruto as a mere human. Naruto, being his friendly self, would probably be curious about Sesshomaru and try to start a conversation. Sesshomaru might respond with cold remarks, but Naruto's persistence could gradually break through his icy exterior.
It's very likely that there is. The fanfiction community is known for its creativity and willingness to experiment with different combinations of characters. In a story where Harry is Sesshomaru's brother, the writer might have to deal with the differences in their respective worlds. For example, Harry comes from a world of wizards and magic that is more in line with a European - style fantasy, while Sesshomaru is from a Japanese - inspired feudal demon - filled world. But that's exactly what makes these crossovers so interesting. Writers can explore how the two characters would interact, how their powers might work together or clash, and how they would navigate each other's worlds.
There are definitely some out there. I've seen ones where Naruto is put in a situation similar to Sesshomaru's, like having to deal with a powerful enemy or a complex moral dilemma in a way that Sesshomaru might. It's really interesting to see how authors blend the two very different universes of Naruto and Inuyasha (where Sesshomaru is from).
One possibility could be that in this fanfiction, female Sesshomaru uses her demon powers to protect Naruto. Maybe she has her own motives, like she sees a kind of potential in Naruto similar to what she once saw in someone else. She could be a very strict but effective guardian, teaching Naruto new combat techniques from her own demon - related knowledge.
One common theme is power. Since both Naruto and Sesshomaru are powerful in their own ways, fanfictions often explore how Naruto would handle Sesshomaru - like powers or how he would adapt to new abilities. Another theme is identity. Naruto has his own strong identity as a ninja, and when combined with Sesshomaru - like traits, it creates an interesting exploration of who he becomes.
One idea could be a crossover where Naruto, Sesshomaru, and a member of the Inuzuka clan are brought together by a powerful magic. They have to work together to defeat a common enemy that threatens all of their worlds. Naruto could use his Rasengan, Sesshomaru his Tenseiga, and the Inuzuka with their unique ninja dog techniques.
Well, one unique aspect is the combination of two very different mythologies. Naruto is based on ninja and Japanese folklore related to that, while Sesshomaru is from Inuyasha's world which has its own set of yokai and feudal Japan elements. When combined in fanfiction, it creates a whole new and exciting world for the readers.