It might be due to some sort of bloodline fusion. Naruto is known for his Uzumaki heritage, but perhaps there was an unexpected encounter with another clan's power that merged with his own, and as a result, one of his eyes turned red as a new and unique ability emerged.
It could be due to a battle injury. Maybe he got into a really tough fight with a powerful enemy, and in the process, lost an eye. For instance, a fight against a rogue Akatsuki member who has a very dangerous eye - related jutsu.
This change in Naruto having one eye could lead to a whole new character arc. Maybe he'd be more self - conscious about his appearance, which could affect his relationships. He might also develop new jutsu that are more suitable for his one - eyed state, like a jutsu that uses his remaining eye's chakra in a more focused way.
He could have enhanced vision powers, like seeing through illusions more easily or being able to detect chakra signatures from a much greater distance. The red eye might act as a sort of sensor, similar to how the Byakugan can detect things, but with its own unique properties.
One common theme is power and its consequences. The red eyes usually come with special powers, and the characters have to deal with how these powers affect their lives. Another theme is identity. Since the red eyes set them apart, they often struggle with who they are in the context of the Naruto world.
One possibility could be through a forbidden jutsu experiment gone wrong. Maybe some rogue ninja was trying to create a super - powered being and Naruto ended up being the subject. The Sharingan was transplanted into him, but only one eye was successful.
In some fanfictions, he might obtain it through a powerful jutsu gone wrong that somehow fuses Uchiha DNA with his own. Maybe during a battle where he's exposed to some strange chakra energy related to the Sharingan.
One example could be a story where a character with red eyes has a unique love story within the Naruto universe. Maybe it's a new character who falls in love with a well - known Naruto character. For instance, a character with red - sharingan - like eyes from a hidden clan could develop feelings for Naruto during a joint mission. They might start off as rivals but gradually realize their love for each other as they face challenges together.
Red eye love can be portrayed through intense gazes. For example, when two characters with a special connection look into each other's eyes, especially if one has red eyes. The red eyes can symbolize mystery or a hidden power, and when they lock eyes with their love interest, it can create a very powerful moment.
Well, in some fanfictions, he might obtain it through a strange encounter. Maybe he stumbles upon an ancient relic during a mission that contains the power of the broken eye dojutsu and it somehow bonds with him.