'archiepiscopally' originates from Late Latin, specifically the word 'archiepiscopus', where the Greek prefix 'arkhi-' meant 'chief' and 'episkopos' (via Latin) meant 'overseer' or 'bishop'.

'archiepiscopally' developed from Late Latin 'archiepiscopus' (via Medieval Latin 'archiepiscopal' meaning 'of or relating to an archbishop') into the English adjective 'archiepiscopal' and then formed the adverb 'archiepiscopally'.

Initially it referred to things 'of or pertaining to an archbishop/archbishopric', and over time it retained that specific sense when used as an adverb to mean 'in an archbishop-like or archiepiscopal manner'.