Old English easterne "of the east, from the east; oriental; of the Eastern Orthodox Church; of the eastern part of the globe," from east + -erne, suffix denoting direction. Cognate with Old Saxon ostroni, Old High German ostroni, Old Norse austroenn. Eastern Shore of Maryland and Virginia so called from 1620s.
superlative suffix of adjectives and adverbs, Middle English alteration (by influence of unrelated most) of Old English -mest, a double superlative, from -mo, -ma (cognate with Latin -mus; compare Old English forma "first," meduma "midmost") + superlative ending -est. Now generally mistaken as a suffixal form of most.
<a href="https://www.etymonline.com/word/easternmost">Etymology of easternmost by etymonline</a>
Harper, D. (n.d.). Etymology of easternmost. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/easternmost