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.
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.
He could practice in secret locations where no one can see him. For example, in an abandoned cave or a hidden part of the forest. That way, no one will know about the new jutsu he's developing.
If Naruto creates a very powerful and dangerous jutsu, some characters might be afraid of him. For example, the villagers who were once suspicious of his Nine - Tails power could again start to fear him. However, his close friends like Sasuke and Sakura would likely trust him and help him control and master the new jutsu.
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.
One challenge could be the complexity of the jutsu itself. His father's jutsu might be very advanced and require a high level of chakra control that Naruto doesn't initially have.
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.
It could speed up his training significantly. If the jutsu scrolls contain advanced techniques, Naruto can learn from them and gain new skills faster than just relying on his regular training with Kakashi. For instance, if there's a jutsu for enhanced strength, he can add it to his arsenal and become stronger in combat.
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.
In fanfic, Naruto may create his own jutsu based on his emotions. His strong will and never - give - up attitude can be translated into chakra - based techniques. For instance, when he's feeling extremely protective of someone, he channels that emotion into his chakra and creates a defensive jutsu. He also might draw inspiration from his memories. Remembering his training sessions with Jiraiya, he could take some of the basic techniques he learned and add his own twist to them, like adding a wind - element boost to a simple physical attack jutsu.