late 14c., "injurious, dangerous," also "absurd, illogical" (senses now obsolete), from Latin inconvenientem (nominative inconveniens) "unsuitable, not accordant, dissimilar," from in- "not, opposite of" (see in- (1)) + convenientem (see convenient). In early 15c., "inappropriate, unbecoming, unnatural;" also, of an accused person, "unlikely as a culprit, innocent." Sense of "troublesome, incommodious, awkward" is recorded from 1650s.
common adverbial suffix, forming from adjectives adverbs signifying "in a manner denoted by" the adjective, Middle English, from Old English -lice, from Proto-Germanic *-liko- (cognates: Old Frisian -like, Old Saxon -liko, Dutch -lijk, Old High German -licho, German -lich, Old Norse -liga, Gothic -leiko); see -ly (1). Cognate with lich, and identical with like (adj.).
Weekley notes as "curious" that Germanic uses a word essentially meaning "body" for the adverbial formation, while Romanic uses one meaning "mind" (as in French constamment from Latin constanti mente). The modern English form emerged in late Middle English, probably from influence of Old Norse -liga.
<a href="https://www.etymonline.com/word/inconveniently">Etymology of inconveniently by etymonline</a>
Harper, D. (n.d.). Etymology of inconveniently. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/inconveniently