Wikipedia's own history section places the origin only as "medieval times," specifically crediting Byzantine Greek and later Ottoman Greek households and tavernes, with no century or decade named. The word meze itself is traced further back, to Ancient Persia, but that is an etymology claim about the WORD, not a dated claim about when the small-dish PRACTICE began; the two should not be conflated into one number.
What would resolve this A dated primary source, a household account, monastic record, market regulation or archaeological find, that places the small-dish-with-drink custom in a specific century within the broad medieval Byzantine window, rather than the general "medieval times" description current secondary sources give.
OpenCulinary and social historyMezze (Wikipedia)