Are there any anime about a psychic character?

Ghost Hunt

While at school, Taniyama Mai and her friends like to exchange ghost stories. Apparently, there is an abandoned school building on their campus that is the center of many ghost stories. During the story, they are interrupted by a mysterious male figure. The person turns out to be Shibuya Kazuya, a 17-year-old who is president of the Shibuya Psychic Research Company. He was called by the principal to investigate the stories surrounding the abandoned school building.

Shinrei Tantei Yakumo

Haruka Ozawa's sophomore year is getting seriously scary. One of her friends is possessed, another has committed suicide and Haruka could be the next one to flunk the still-breathing test. Her only way out of this potentially lethal dead end? Yakumo Saito, an enigmatic student born with a mysterious red eye that allows him to see and communicate with the dead. But the deceased don't always desist and some killers are more than ready to kill again to keep dead men from telling any more tales. That doesn't stop Haruka's knack for digging up buried secrets, and there's even more evidence of bodies being exhumed by both Yakumo's police contact and an investigative journalist with a newly made corpse in her closet! Can this pair of anything but normal paranormal detectives solve the ultimate dead case files or will they end up in cold storage themselves?

blue Exorcist

Humans and demons are two sides of the same coin, as are Assiah and Gehenna, their respective worlds. The only way to travel between the realms is by the means of possession, like in ghost stories. However, Satan, the ruler of Gehenna, cannot find a suitable host to possess and therefore, remains imprisoned in his world. In a desperate attempt to conquer Assiah, he sends his son instead, intending for him to eventually grow into a vessel capable of possession by the demon king.

Noragami

a middle school girl, Hiyori Iki, supposedly saves Yato from a car accident, taking the hit for him. Remarkably, she survives, but the event has caused her soul to become loose and hence able to leave her body. Hiyori demands that Yato return her to normal, but upon learning that he needs a new partner to do so, reluctantly agrees to help him find one. And with Hiyori's help, Yato's luck may finally be turning around.