This story from Vanity Fair is the most interesting one I've seen regarding demons and psychiatry: https://archive.vanityfair.com/article/2016/12/battling-the-devil

It includes commentary from four Columbia University psychiatrists on a video of a Catholic exorcism, as well as an account from Jeffrey Lieberman (Chairman of the Department of Psychiatry at Columbia University) on a case that he said gave him pause:

"One night, I went to see [the patient] and then conferred with a colleague, and afterwards I went home, and there was a kind of a blue light in the house, and all of a sudden I had this piercing pain in my head, and I called my colleague, and she had the same thing, and this was really weird. The girl's family was prone to superstition, and they may have mentioned demon possession or something like that, but I obviously didn't believe it, but when this happened I just got completely freaked out. It wasn't a psychiatric disorder—you want to call it a spiritual possession, but somehow, like in The Exorcist, we were the enemy. This was basically a battle between the doctors and whatever it was that afflicted the individual."