So basically, no one knows the correct spelling or where it came from, but in true redditor fashion everyone insists it’s the more intellectual option and everyone who disagrees is an idiot.
I'd not seen the spelling "sike" until today; but I've been spelling it "psych" since I was in grade school in the early 70's. Definitely derives from "psyching someone out", i.e., confusing them or tricking them (in that I first heard "psych" as shorthand for "psych out"). I wouldn't be at all surprised if it's older than that.
I use "psych" too. Bummed me out when I learned "sike" was the correct spelling.