What is the X in X-mas?
in native (derived from Old English) words, it most commonly represents Old English an "on" (see a (2)), as in alive, asleep, abroad, afoot, etc., forming adjectives and adverbs from nouns; but it also can be Middle English of, as in anew, abreast (1590s); or a reduced form of Old English past participle prefix ge-, as in aware; or the Old English intensive a-, as in arise, awake, ashame, marking a verb as momentary, a single event. In words from Romanic languages, often it represents Latin ad- "to, at."
[I]t naturally happened that all these a- prefixes were at length confusedly lumped together in idea, and the resultant a- looked upon as vaguely intensive, rhetorical, euphonic, or even archaic, and wholly otiose. [OED]
prefix meaning "not," from Latin a-, short for ab "away from" (e.g. avert), or its cognate, Greek a-, short for apo "away from, from," both cognate with Sanskrit apa "away from," Gothic af, Old English of (see apo-).
prefix meaning "not," from Greek a-, an- "not," from PIE root *ne "not" (see un-).
a- or an-
Without; not: acellular.
A prefix meaning "without" or "not" when forming an adjective (such as amorphous, without form, or atypical, not typical), and "absence of" when forming a noun (such as arrhythmia, absence of rhythm). Before a vowel or h it becomes an- (as in anhydrous, anoxia).