I know that the most common writing media for the Latin language were papyrus, stone, wax and wood tablets. But, are there any clay tablets preserved to this day that are written in Latin?
All I can find in my research are tablets in cuneiform writing, so from other civilizations.
Sort of. Bricks for building were often stamped with words indicating who made them and oversaw their production. But this probably isn't what you're looking for. They also sometimes wrote on shards of broken pottery ("ostraca") for short-term notes, since it was cheaper than papyrus for some purposes. But I don't think this is what you're looking for either.
Clay tablets were used in Mesopotamia because clay was everywhere, and their writing system developed from stamping clay tokens into clay envelopes, so it was well-suited for, well…writing on clay.
But the Romans had papyrus and ostraca (and wax) for writing ephemeral things, and stone for more permanent things. There was no real reason for a Classical-era Roman to carry a ball of clay around to write on.
