The ē reading is literary and now mostly survives as a bound morpheme in 阿谀, 阿谀奉承, and 刚正不阿. Solo verb use is rare in modern speech.
culture
The Buddhist invocation 阿弥陀佛 (Amitābha Buddha) takes ē in the dictionary tradition - a Sanskrit transliteration that kept the literary reading because it entered Chinese through scripture, not colloquial naming.
Left-side 阝 is the mound radical 阜 in compressed form - always meaning hill or earthwork on the LEFT (right-side 阝 is the different city radical 邑). Indexes 阿 with 陡, 阴, 阳. Original sense was a sheltered curve under a hill.
Right is 可 supplying the sound - kě drifting to ā through k/zero-initial alternation. Same phonetic family as 河, 何, 哥. The familiar-prefix sense detached from the original hill-nook meaning.
