Old English feccan, apparently a variant of fetian, fatian "to fetch, bring near, obtain; induce; to marry," probably from Proto-Germanic *fatojanan (cf. Old Frisian fatia "to grasp, seize, contain," Old Norse feta "to find one's way," Middle Dutch vatten, Old High German sih faggon "to mount, climb," German fassen "to grasp, contain"). Variant form fet, a derivation of the older Old English version of the word, survived as a competitor until 17c. Related: Fetched; fetching.
"apparition, specter, a double," 1787, of unknown origin (see OED for discussion).