imp: [OE] Old English impe meant ‘new shoot, sapling’. Its ultimate source was medieval Latin impotus ‘graft’, a borrowing from Greek émphutos, which itself was an adjective derived from the verb emphúein ‘implant’. In the early Middle English period it began to be transferred from plants to people, carrying its connotations of ‘newness’ or ‘youth’ with it, so that by the 14th century it had come to mean ‘child’.
And in the 16th century, in a development similar to that which produced the now obsolete sense of limb ‘naughty child’, it was applied to ‘mischievous children, children of the Devil’, and hence to ‘mischievous or evil spirits’.
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]