Sure. One could have the power of flight, like Angel. Or the power to generate and control electricity, similar to Electro but in a mutant form. Another possibility is the power of invisibility, which would be very useful for sneaking around or spying on enemies.
One mutant power often explored in Star Trek fanfic is energy manipulation. A character might be able to generate and control various forms of energy, such as plasma or subspace energy. This could be used for offensive purposes, like shooting energy blasts at enemies, or for more practical uses like powering up a damaged ship's systems. Another interesting power is the ability to phase through solid objects, which could be used for stealth or to access restricted areas. There could also be mutants with the power of time manipulation, being able to slow down or speed up time in a local area.
One possible power for Harry as a mutant could be the ability to manipulate time. He could slow it down, speed it up, or even travel through it. This would give him an edge in battles and also open up new plot possibilities, like trying to prevent certain disasters or change the course of events in the fanfiction world.
Mutant powers can disrupt the status quo in the Star Trek universe in fanfic. For example, if a mutant has the power of teleportation without the need for transporter technology, it could undermine the importance of starship transportation and exploration as we know it in the series. It could also change the power dynamics between different species and factions. If a mutant has a very powerful offensive ability, it might tip the balance of power in a conflict.
He could have the power of technopathy. Since Tony is already so connected to technology, as a mutant, he might be able to directly communicate with machines and control them with his mind. This would give him an even greater edge in creating and operating his Iron Man suits.
Well, he could have water - based mutant powers. Since Percy already has a strong connection to water in his original story, as a mutant, he might be able to control water on a molecular level. He could create water out of thin air or turn water into ice instantly for offensive or defensive purposes.
If Naruto had mutant powers in fanfiction, his confidence would likely soar. He'd no longer be the underdog constantly trying to prove himself. His mutant powers would make him stand out even more, and he might become a bit more arrogant at first. But as he faces new challenges, he would learn to use his powers responsibly.
I can recommend some classic novels such as Doomsday Powers, Mr. Zombie, Doomsday Master, etc. These novels told the story of the protagonist's survival and struggle after the apocalypse by awakening his supernatural abilities and courage. These novels were highly readable and interesting, and could give readers a lot of inspiration and insight. I hope you will like these novels.
One possible storyline could be Naruto's mutant power being the ability to control all forms of nature energy without the need for training. This would make him extremely powerful and feared in the ninja world. Another could be that his mutant power is related to instant teleportation, allowing him to appear anywhere in an instant, which would change the dynamics of battles and missions.
If Spider - Man had mutant powers in fanfiction, his origin story might be different. Instead of being bitten by a radioactive spider, he could be born with his powers. This would change his relationship with the scientific community. For example, he might not be as interested in science as the original Spider - Man. His powers could also be more uncontrollable at first, leading to different challenges in learning to use them.