Any correspondence or communication written in the form of a letter or series of letters is said to be epistolary.

They've gone out of fashion now, but in the eighteenth and nineteenth centuries the "epistolary novel," written in the form of fictional letters to and from various corespondents, was all the rage. One of the most famous such novels (or at least part epistolary) is Bram Stoker's "Dracula." Epistolary is related to the word epistle, a fancy term for "letter."

Definitions of epistolary

adj written in the form of or carried on by letters or correspondence

“an endless sequence of epistolary love affairs”
used of spoken and written language

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