Mitsuki is one of Misaka's classmates who has a pretty obvious crush on her—though she's definitely not interested. When he won't take the hint, she and Touma fake being a couple to get him to back off. He's also the grandson of their school's principal, which probably doesn't help his ego much.
His ability is Level 4 Telekinesis, letting him manipulate objects from a distance. What's interesting is that he can apply this power to his own body too, not just external stuff. This actually saved his life at one point: when he was severely injured, he used telekinesis to petrify his own cells, essentially putting himself into a state like cryogenic stasis—frozen and unable to move, but also completely protected from further harm.
The sketchy part of his story comes from Volume 5. He got arrested after harassing Misaka, but here's the twist: it wasn't actually him. A magician named Etzali had borrowed his appearance as a disguise. Before the main story kicks off, Etzali had already beaten and imprisoned the real Mitsuki about a week earlier. Touma eventually figured out the switch because Etzali made a dumb mistake—he supposedly helped Touma with summer homework, but the real Mitsuki wouldn't have been smart enough to do that. Kuroko's investigation later revealed that Mitsuki actually cheats on all his exams using a thin layer of his telekinetic ability on the computer screen to sense the heat and radiation, then reverse-engineer the answers.
After everything goes down, Mitsuki's fate stays pretty vague across the series. Etzali kept his appearance borrowed, and Mitsuki's whereabouts become unknown. Though the story does eventually confirm he escaped from his imprisonment without any life-threatening injuries.
Content compiled by AnimeList.moe from publicly available sources.