Perhaps during a time - travel adventure in a fanfiction, Naruto got into a fight in the past and lost his eye. When he returned to his own time, he kept the eyepatch as a memento of his journey through time and also as a symbol of the knowledge he gained from that experience.
Maybe he was attacked by a rogue ninja with a special weapon that damaged his eye. This would be a tragic event that could change his perspective on the ninja world and his role in it. The eyepatch would then be a constant reminder of that fateful encounter.
There might be a fanfiction where Naruto's eyepatch is actually a magical or chakra - infused item. It could have been given to him by an ancient sage, and it gives him special powers like enhanced perception or the ability to see through genjutsu more easily. This would add an exciting new aspect to his character.
It could be that the wolf is a reincarnation of an ancient protector of the ninja world. It was waiting for the right person to bond with, and Naruto, with his strong will and desire for peace, was the chosen one. So they became partners.
Perhaps in this fanfiction, Naruto travels back in time. He goes to a time when the world was being formed, and through his unique chakra, he gives birth to the Nine - tails. This could be part of a grand plan to ensure balance in the future ninja world, and he is the only one with the power to do so.
In the fanfiction, a possible backstory could be that Naruto, after achieving great power and peace in his own time, decided to use his abilities to explore the past. During this exploration, he accidentally or purposefully got involved in the lives of his ancestors. He might have fallen in love with a woman from the Uzumaki clan in the past and had children. These children then passed on their genes through generations until Kushina was born. It could also be that there was some sort of experiment by an ancient shinobi that went wrong or right (depending on how you look at it). This experiment somehow connected Naruto's future self to be Kushina's grandfather by altering the fabric of time and family relations in a very strange way.
One origin could be a genetic mutation within the Uzumaki clan that has been dormant for generations. Naruto, being an Uzumaki, could be the first in a long time to have this mutation manifest as claws. Or it could be due to a curse placed on him by an enemy. However, instead of weakening him, the curse gives him the claws which he then learns to use to his advantage. It could also be a gift from a powerful sage or spirit that he encounters during one of his adventures, seeing the potential in Naruto and bestowing him with the ability to have claws for a specific purpose like protecting the village or fighting a greater evil.
One possibility is that it could be related to some sort of new power or transformation. Maybe it's a result of an experiment gone wrong or a connection to a long - lost bloodline. For example, it could be a remnant of an ancient clan's ability that has been dormant in Naruto all this time.
Maybe he had some bad experiences with weaklings who let him down in crucial moments. For example, a weak comrade could have failed to protect someone important, and that made Naruto start to dislike those he considered weak.
The beehive could be a plot device to introduce new characters or conflicts. For example, the beekeeper who owns the beehive could be an important character, or there could be a conflict where someone wants to destroy the beehive and Naruto has to protect it. This would add new layers of story and character development in the fanfiction.
One significance could be related to his power. Fangs might symbolize his hidden strength, like his jinchuriki powers. It gives a more visual representation of the beast within him.
Perhaps it was a gift or a curse from some powerful being. For example, a god or a demon could have bestowed this third eye upon Naruto for some purpose, either to help him in his journey or to make his life more difficult with new powers that come with their own challenges.