word-forming element meaning "not, opposite of, without" (also im-, il-, ir- by assimilation of -n- with following consonant, a tendency which began in later Latin), from Latin in- "not," cognate with Greek an-, Old English un-, all from PIE root *ne- "not."
In Old French and Middle English often en-, but most of these forms have not survived in Modern English, and the few that do (enemy, for instance) no longer are felt as negative. The rule of thumb in English has been to use in- with obviously Latin elements, un- with native or nativized ones.
1610s, "allowable," from French admissible, from past participle stem of Latin admittere "allow to enter, admit, give entrance," from ad "to" (see ad-) + mittere "let go, send" (see mission). Meaning "capable of being allowed entrance" is from 1775; specific sense of "capable of being used in a legal decision or judicial investigation" is recorded from 1849.
<a href="https://www.etymonline.com/word/inadmissible">Etymology of inadmissible by etymonline</a>
Harper, D. (n.d.). Etymology of inadmissible. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/inadmissible