Not to get TOO technical, but Psionics (as a concept, not the name) originated neither in pure Sci-fi nor in pure Fantasy, but more in horror...the two genres' bastard love-child.
The evil mesmerist, dominating the minds of lesser men...The pyrokineticist looking at you and going "Burn..."...flinging objects across a room with a thought...
this was all fodder for horror/pulp for decades before either Sci-Fi or Fantasy picked up on it.
Not that anyone will let that fact sway them either way, of course.
And if we're talking pseudo-science...
Look at the way alchemy is depicted both in fantasy and in its own real texts- its a "scientific" process with fantastic elements. Some supplements have "Artificers"...and who hasn't used/fought against some kind of "Clockwork" opponent?