Sasuke could be a candidate. Given their complex relationship, Sasuke might find a way to give Naruto a new arm as a way to atone for their past differences. He could have discovered some rare medical ninjutsu during his travels or come across a powerful artifact that he uses to create a new arm for Naruto.
Maybe Orochimaru. Despite being a villain in the past, he is a master of forbidden jutsus and experiments. He could see Naruto as an interesting subject and give him a new arm with some dark powers, which Naruto would then have to learn to control for the greater good.
Well, it could be that he got it as a gift from some super - advanced ninja technology group in the fanfiction world. Maybe they saw his need for an extra weapon or tool during battles and decided to equip him with a metal arm.
One special ability could be enhanced strength. The metal arm might be able to deliver much more powerful punches than his normal arm, allowing him to break through tough defenses more easily.
Maybe he was protecting someone in Wave. He's always the self - sacrificing type, so he could have put himself in harm's way to save a villager or a friend.
Naruto may become more cautious. With a prosthetic arm, he realizes his vulnerability more. He might start to think more strategically before jumping into battles. For example, in a fight, he won't just rely on his brute strength but use the unique features of his prosthetic arm to his advantage.
Well, in some fanfictions, he might get it from a skilled ninja prosthetics maker. This maker could be someone who specializes in creating artificial limbs for ninjas who have lost their arms in battle.
One possible fanfiction could be about Naruto's right arm gaining a new and mysterious power. Maybe it starts to glow with an unknown chakra, and he has to figure out how to control it without losing himself. It could be a power that has a connection to an ancient ninja clan's secret technique.
Another possibility is that Naruto and Yang have a special bond. This bond could be formed through shared experiences, like they both went through a difficult training together or survived a life - threatening situation. Because of this special connection, Naruto feels indebted to Yang or simply values Yang's life more than his own arm.