Naruto's reaction could be complex. On one hand, he would be happy to find someone else from his clan. He has always been proud of his Uzumaki heritage despite not knowing much about it at first. But on the other hand, he might be a bit cautious. Karin has been associated with some not - so - good groups in the past. However, overall, his positive nature would probably lead him to approach Karin with an open mind and try to build a connection with her based on their shared Uzumaki roots.
At first, Naruto might be shocked and confused. He would probably wonder why his own clan would do such a thing to him. He might feel a deep sense of betrayal, especially since he has always longed for a family and a sense of belonging within the Uzumaki clan. But being Naruto, he would soon turn his confusion and pain into determination. He would vow to prove himself and show the clan that they were wrong to exile him.
It depends on the specific plot of the fanfic. Sometimes he could be on a secret mission, in a hidden village, or facing a new challenge in an unknown location.
The Legend of Uzumaki Hiroto was a derivative work of Naruto, which told the story of Uzumaki Hiroto's growth and the stories of other characters. Uzumaki Boto Legend was different from the original Naruto Naruto Shimbun Legend, so it was considered an independent manga.
Naruto would probably first try to find a peaceful solution. He has always been one to believe in the power of friendship and understanding. He might try to talk to the leaders of both villages, like Gaara in the Sand, to find out what's really going on and resolve the misunderstandings.
He is probably very excited. Naruto has always been eager to learn new things and become stronger. Finding an Uzumaki scroll means he has the chance to discover something unique about his own clan, so he would be filled with anticipation.
In many fanfictions, Naruto might obtain the Uzumaki sword through a hidden inheritance. Maybe it was left behind by an ancient Uzumaki clan member and Naruto discovers it in a secret location, like an old, forgotten Uzumaki shrine.
Well, he could start a family with Hinata and have lots of kids, passing on his Uzumaki bloodline. Then, he could encourage his friends who have some Uzumaki connection, like Karin, to also have families and pass on their Uzumaki genes. He could also set up a school or training center in the Uzumaki land, teaching the Uzumaki ways of life and ninjutsu, which would attract orphans or those who want to be part of the Uzumaki clan.
In many fanfictions, Naruto's reaction is a mix of shock and determination. The shock comes from finally learning about his clan, and the determination is to uphold the Uzumaki name. He could start wearing something that represents the Uzumaki clan, like a symbol on his clothing. He also may become more protective of the Uzumaki secrets and legacies he discovers.