imp (n.) Look up imp at Dictionary.com
Old English impe, impa "young shoot, graft," from impian "to graft," probably an early West Germanic borrowing from Vulgar Latin *imptus, from Late Latin impotus "implanted," from Greek emphytos, verbal adjective formed from emphyein "implant," from em- "in" + phyein "to plant" (see physic).

Sense of "child, offspring" (late 14c.) came from transfer of word from plants to people, with notion of "newness" preserved. Modern meaning "little devil" (1580s) is from common use in pejorative phrases like imp of Satan.
Suche appereth as aungelles, but in very dede they be ymps of serpentes. ["The Pilgrimage of Perfection," 1526]