'border-adjacent' originates from Modern English as a compound of 'border' and 'adjacent'. 'Border' comes ultimately from Old French bordure ('edge, border'); 'adjacent' comes from Latin 'adjācēns' (from 'ad-' meaning 'to/toward' + 'iacēre' meaning 'to lie').

'border' passed from Old French bordure into Middle English (bordure, bord(e)re) and became modern English 'border'; 'adjacent' came from Latin adjācēns through Late Latin/Old French into English as 'adjacent'. The compound 'border-adjacent' is a modern English descriptive formation (noted in 20th-century usage) combining these elements.

Individually, 'border' originally referred to an edge or boundary and 'adjacent' meant lying near; together as the compound 'border-adjacent' the phrase came to be used specifically to describe something located next to a political or administrative border (and by extension, things figuratively near a dividing line).