Naruto's shadow clone jutsu could have a new twist. Instead of just creating clones for battle, the clones could be used to perform tasks around the One Punch Man universe, like helping to rebuild after a villain attack. And his ability to use nature energy could be combined with Saitama - like strength, allowing him to deliver punches that not only have physical force but also some kind of energy - based impact.
His ninjutsu might be enhanced. For example, his Rasengan could gain new properties due to the influence of Campione powers. His speed and strength, which were already considerable in the Naruto world, could be further increased. Maybe his ability to sense danger, which was related to his ninja training, could be upgraded to a more supernatural level in the Campione world.
Another possibility is that Naruto, in this fanfiction, is given a power similar to Saitama's. He then has to deal with the consequences of having such overpowered abilities. He might struggle with not being able to have a real challenge in battles anymore, just like Saitama. And he could try to find a new purpose in life, perhaps using his new strength to help the people in the One Punch Man universe in a more efficient way than he did in his own world.
Well, in these fanfictions, characters' abilities often change due to the influence of the gamer elements. The gamer character may be able to distribute stats like in a role - playing game. So, they could boost a character's intelligence stat, which might then allow that character to come up with more complex battle plans. Another way is through item acquisition. A character might find a game - item that gives them temporary flight ability or enhanced vision, completely changing their combat capabilities in the One Punch Man world.
His abilities would become more lethal. Instead of using his Rasengan to just defeat opponents, he might use it to kill. His speed and stealth would be enhanced for more effective assassinations. His ability to gather information, like he did as a ninja, would be used in a more sinister way to track down his targets.
His ability to move would change drastically. Vader has his slow, yet intimidating, mechanical walk. Naruto might adopt a similar gait as he becomes more like Vader. In terms of combat, Naruto's Rasengan could be combined with the dark side of the Force. It could become a more destructive and corrupting attack, maybe with a black, swirling energy around it. Also, his ability to sense others, which was based on chakra before, could now be a more Force - like sense, allowing him to detect enemies even through walls and over long distances.
Yes, there likely is. The Naruto and One Punch Man fandoms are both quite large, and it's common for fans to create crossover fanfictions. These crossovers can be really interesting as they combine the unique elements of both universes, like Naruto's ninja skills with Saitama's one - punch power.
His relationships would change a great deal. His friends might feel a bit overshadowed by his new power. For instance, Sasuke might feel even more compelled to compete with Naruto, but also realize the futility of it. His relationship with Sakura could become a bit strained as she might be in awe and a bit intimidated by him now.
His strength could increase exponentially. He might be able to lift boulders with ease or break through the toughest defenses. His speed could be so great that he becomes a blur to his enemies. Also, his reflexes would be lightning - fast, allowing him to dodge attacks more effectively.
Genos would probably be even more in awe of Saitama. He already idolizes him, but with Saitama being S - Class, Genos might see him as even more untouchable. He could become more protective of Saitama's new status, trying to fend off any detractors or those who might try to take advantage of Saitama.
Another idea is that Naruto, curious about other powerful beings, uses a jutsu to travel to the One Punch Man universe. There, he would be amazed by Saitama's strength. Naruto could try to learn from Saitama how to be so effortlessly strong, but Saitama would probably just shrug it off and say there's no special trick. They could team up to fight some of the monsters in Saitama's world, with Naruto using his ninjutsu and Saitama just punching things away.