Yes, there might be such fanfics in the Naruto fanfic community. Some fans like to create unique family relationships in their stories, and making Naruto and Shisui brothers is an interesting concept that could lead to many different plotlines and character interactions.
In this kind of fanfiction, Naruto might obtain Shisui's brother's Sharingan through some unforeseen events. Maybe Shisui's brother sacrifices himself and entrusts his Sharingan to Naruto. As for new abilities, it could enhance Naruto's perception skills like being able to see through genjutsu more easily and also improve his combat awareness in battles.
One possible plot could be that Naruto grows up with a different understanding of the Uchiha clan because of his connection to Shisui. He might be more involved in Uchiha affairs from an early age. For instance, he could try to prevent the Uchiha massacre, using his and Shisui's combined influence.
Another ability Naruto could gain is a deeper understanding of genjutsu. Shisui was very proficient in genjutsu, especially with his Sharingan. Naruto, being his brother, could have a natural aptitude for genjutsu. He could learn to break through stronger genjutsu more easily and also use more advanced genjutsu himself. This would be a significant change as Naruto was not originally known for his genjutsu skills, but with this new connection, he could become a more well - rounded ninja.
In this scenario, Naruto being Shisui's brother would mean he might have grown up with a different kind of training. Shisui was highly skilled in the ways of the ninja. Naruto could have learned some of his stealth and combat techniques at an earlier age. This would make him an even more formidable opponent. Moreover, it could have an impact on the Akatsuki's plans. They were after the Sharingan, and if Naruto was related to Shisui, they might target him differently. It could also change the way the village of Konoha views Naruto. He would have a stronger connection to the Uchiha, which could either make them more suspicious of him or more protective, depending on how the story unfolds.
In this fanfiction, a likely plot development could be that Naruto starts to experience strange visions or memories from Shisui's brother due to the Sharingan. This causes him to go on a journey to discover the secrets behind these visions. Also, the Leaf Village elders might become suspicious of Naruto's new power and try to keep an eye on him, which creates internal conflicts within the village.
Another plot could involve Naruto and Shisui going on missions together. Since Naruto is often underestimated in the original series, Shisui's presence as his brother might make others take him more seriously. They could form a powerful duo, with Naruto's brute strength and Shisui's Sharingan abilities complementing each other, and face off against powerful enemies like Orochimaru or Akatsuki members.
Perhaps the plot twist is that Shisui faked his death not just to protect the village in the general sense, but specifically to keep Naruto safe. He knew of Naruto's importance as the Jinchuriki of the Nine - Tails and his relation to Naruto as a brother. So, he went into hiding and has been secretly guiding Naruto from the shadows all along. This would add a whole new layer to Naruto's journey and the events that have unfolded in the series so far.
The relationship would have a major impact on Naruto's character development. Knowing he has an Uchiha brother, he might study more about the Uchiha ways and culture. This could lead to new jutsu combinations, like combining his Rasengan with some Uchiha - style fire jutsu. Emotionally, it would give him a stronger family bond, which was something he always desired. In the overall Naruto universe, this could inspire other characters to look beyond clan differences and strive for unity, as Naruto and Shisui's relationship would be a symbol of bridging gaps between different groups.
Their relationship could change the perception of the Uzumaki and Uchiha clans. Traditionally, the two clans haven't had much interaction in the original story. But as brothers, Naruto and Shisui could bridge that gap. This might lead to new alliances and political changes within the Hidden Leaf Village.