In some fanfics, it could be through a curse. Maybe an old, forgotten curse targets Naruto and as a result, he gains an eye bloodline. Another way is through some sort of experiment gone wrong. Scientists or rogue ninjas might be experimenting with bloodlines and Naruto accidentally gets affected.
In some fanfics, Naruto absorbs the bloodline through a special jutsu. For example, he might find an ancient scroll that contains a jutsu allowing him to transfer and absorb the genetic traits related to a bloodline.
Well, a popular one could be 'Naruto: The Bloodline Revolution'. In this, Naruto's eye bloodline might be a combination of different clans' traits. It could make him see chakra in a whole new way or have some sort of time - space related abilities. Then there's 'The Hidden Eye of Naruto' where his eye bloodline is hidden from everyone until a certain event triggers its awakening and he has to learn to control it quickly. And 'Naruto's Blood - Eyed Destiny' where his new eye bloodline is seen as a sign of a great prophecy.
In many fanfics, when Naruto gets banished because of his bloodline, it completely alters his relationship with the village. Instead of being the hero they come to accept, he becomes an outcast. This changes the power dynamics as he has to rely on his own strength and his bloodline abilities more than ever, without the support of the village like in the original story.
He might use some special jutsu or seals. For example, he could use a sealing technique to suppress the signs of his bloodline. This way, others wouldn't be able to detect it through normal means like sensing chakra.
Well, it could be due to a powerful enemy attack during a fight in Wave. Maybe an enemy with a sharp weapon or some dangerous jutsu managed to strike Naruto's eye.
Well, the Saiyan bloodline can change Naruto's character in multiple ways. Firstly, his sense of pride gets a boost. Saiyans are proud warriors, and Naruto starts to take more pride in his abilities. He may become more confident, not just in his ninja skills but also in his physical strength. Secondly, his temper could be shorter. Saiyans are known for their short tempers when provoked, and Naruto might show this trait more often. He could get angry more easily, especially if someone challenges his newfound Saiyan - related powers. However, he still has his ninja values deep down, so there's an internal struggle between his Saiyan - influenced self and his original ninja self.
In some fanfictions, Naruto might obtain the bloodline through a magical or spiritual connection with the Fem Kyuubi. Maybe during a moment of extreme danger or a special ritual where the power of the Fem Kyuubi is transferred to him, allowing him to gain a new bloodline.
Well, if Naruto can remove bloodline in a fanfic, it could drastically change the power balance. For one, clans that rely on their bloodline abilities would be at a great disadvantage. Their unique skills, which usually give them an edge in battles and in the shinobi world in general, would be nullified. This would likely lead to a shift in the political and social structure within the Naruto universe of the fanfic. Clans might have to find new ways to assert their influence and power, and new rivalries could form between those who support Naruto's new ability and those who oppose it.
The 'perverted bloodline' often introduces an element of the unknown and mystery. This affects the plot as other characters may be curious or afraid of it. The character with the bloodline may be ostracized or idolized, depending on how the fanfic is written. This leads to different relationships forming, such as alliances or rivalries. As the story progresses, the discovery of the origin and full potential of the bloodline can be a central plot point, with twists and turns as new information is revealed.
In some fanfictions, Naruto might get the scar on his eye during a particularly intense battle with a powerful enemy. Maybe it was a close encounter with a rogue ninja's weapon that managed to leave a mark on his eye area.