1391, from
amidde (12c.), from O.E.
on middan "in the middle," from dative singular of
midde "mid, middle."
Amidde became
amyddes (13c.) with adverbial genitive ("in the middle of") and acquired a parasitic
-t (first attested 1565), probably by association with superlatives in
-st. Cf. L.
in medio, Gk.
en meso, both originally adjective phrases which evolved to take the genitive case.
"There is a tendency to use amidst more distributively than amid, e.g. of things scattered about, or a thing moving, in the midst of others." [OED]
Amidships is attested from 1692, though the adverbial genitive suggests a much earlier origin.