late 14c., "non-essential," from Old French accidentel or directly from Medieval Latin accidentalis, from Latin accidentem "an accident, chance" (see accident). Meaning "outside the normal course of nature" is from early 15c.; that of "coming by chance, unintentional" is from 1570s. Accidential (1811) sometimes serves now in the sense "characterized by non-essential qualities" and goes with accidence.
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/accidentally">Etymology of accidentally by etymonline</a>
Harper, D. (n.d.). Etymology of accidentally. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/accidentally