In a fanfic, Naruto's teleportation jutsu could be different in terms of its range. Instead of having a set range, it could be based on his current chakra level. So, if he's full of chakra, he can teleport across the entire ninja world, but if he's low on chakra, it's only a short - distance teleport. Also, the jutsu could have a side effect. For instance, every time he teleports, he has a brief moment of disorientation. This would add an interesting element to battles and his overall use of the jutsu. Moreover, the teleportation could be linked to specific landmarks. He can only teleport to places he has a strong mental image of, like his home in Konoha or the training grounds where he practiced with Kakashi.
Well, in a fanfic, a really cool plot for Naruto's teleportation jutsu could be that he discovers a new form of the jutsu that allows him to teleport groups of people instead of just himself. This could lead to some amazing rescue missions. Or, perhaps he teleports to a hidden village that no one knew existed and has to deal with their unique culture and jutsu. Also, he might use the jutsu to teleport objects instead of just himself, which could open up all kinds of strategic possibilities in battles.
He could potentially learn the Flying Thunder God Technique. It's a very powerful jutsu that Minato was famous for. Naruto's already fast with his Sage Mode and Nine - Tails Chakra, and this would make him even more formidable in battle.
Well, in certain fanfic scenarios, Naruto could learn paper jutsu as a result of some experimental training. For example, he might be trying to combine different elements of his existing jutsu and accidentally discovers a way to manipulate paper. It could be that his chakra takes on a new form during a particularly intense training session and he realizes he can control paper with it.
Maybe he found some hidden scrolls left by his mother. These scrolls could have contained the details of her jutsu. Naruto, being the curious and determined ninja he is, would have studied these scrolls carefully and learned the jutsu.
Well, it could be the Uzumaki Chain jutsu. In the Naruto lore, the Uzumaki clan had some unique abilities and the chain jutsu was one of them. His mother Kushina was from the Uzumaki clan, so it's possible that's the jutsu he learned in the fanfiction.
In a fanfic, Naruto might be motivated to learn medical jutsu because he realizes that his strength alone isn't always enough. He's been in situations where he couldn't protect everyone, and medical jutsu would be another way to ensure their safety. Also, he may want to prove himself in a different area. He's known for his combat skills, but learning medical jutsu would show his growth and ability to adapt.
Well, in many such fanfictions, Naruto might start learning his father's jutsu when he discovers some hidden scrolls or when a mentor who knew his father decides to teach him. Maybe it could be someone like Jiraiya who reveals some secrets about his father's techniques.
There could be a jutsu that allows for instant teleportation across long distances. This jutsu might be a new discovery in the fanfiction world, perhaps created by a character who has been experimenting with space - time ninjutsu. They might use it to quickly get in and out of battles or reach far - off places in a blink.
He might learn Orochimaru's signature snake - related jutsu, like the Hidden Shadow Snake Hands. This jutsu allows the user to summon snakes from their sleeves or other hiding places to attack opponents.