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 some fanfictions, Naruto's eye bloodline is linked to a long - lost clan. His eyes hold the key to unlocking ancient secrets and powers. This often leads to him going on a quest to find out more about his heritage and the true nature of his eyes. For example, he might discover that his eyes can open portals to other dimensions which is a really cool concept.
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.
It could also be a result of a unique encounter with a powerful entity. For instance, if Naruto entered a mysterious realm where the essence of Haku's bloodline was stored, and some sort of transference occurred, perhaps due to Naruto's own unique chakra nature. This could lead to him obtaining Haku's bloodline.
Power discovery. Since the Uzumaki bloodline is powerful, a common theme is Naruto finding out about his hidden powers. For example, he might discover a new form of chakra control or a special jutsu related to his Uzumaki heritage.
One interesting plot could be that Naruto discovers his hidden bloodline gives him the ability to control time in small increments. This allows him to dodge attacks more easily and plan his counter - attacks more effectively.
It could be a rogue ninja from a forgotten clan who is jealous of Naruto's new - found power from his hidden bloodline. This antagonist might try to steal Naruto's bloodline ability for himself.
A really interesting 'naruto has uzumaki bloodline fanfic' is 'Naruto: The True Uzumaki'. This fanfic explores the political implications of Naruto having the Uzumaki bloodline. It shows how different villages react to the fact that Naruto has such a powerful and rare bloodline, and how Naruto has to navigate through all the politics while still being true to himself.
There are also fanfictions where a bloodline is created through some sort of experimental jutsu. For example, a bloodline that allows the user to transform into different elements at will. This would give the character an edge in combat as they could adapt to any situation by changing their form.
He might gain the ability to manipulate ice like Haku. This could be a very useful addition to his existing skill set, especially in battles against fire - type opponents. He could create ice clones instead of the regular shadow clones, which would be more durable in certain situations.