Bayek and later his wife Aya are described as Medjays in the game. The Medjay were simply the inhabitants of the region of the Medja during the Old and Middle Kingdoms (c. 2700-1500 BC). Later, during the New Kingdom (c. 1500-1050), the word Medjay become a common word for a kind of sheriff, as a lot of those were first recruited among the people from Medja.
However, it is very unlikely Bayek and Aya could have been Medjays, since the institution disappeared with the New Kingdom at the end of the second millenary BC, while the game takes place a thousand years later. Nice try Ubi 😉