I'm not sure I can actually come up with any, because I know how frail human minds can be. My prior that I'm insane is higher than my prior that magic exists, and I can't think of any evidence for the second that isn't at least as strong evidence for the first.

(Here, I am assuming that by psychic powers we're talking about magic, rather than unarticulated intuition, which I believe can exist; I also expect I would adapt to being insane pretty quickly, and would react as if it were reality, but would expect it more likely that I'm gibbering in a mental institution than that I've been transported to Narnia.)