What Is This Unknown Greek... Token?

It may be a theatre token, but perhaps not ancient Greek.
It may be medieval, or of the renaissance period.

I notice a greenish patina, and so I am suspecting that it may be an alloy of copper, lead and tin, where the copper proportion may be well below 50%.

Does the metal seem to be quite soft, much like pewter?

It looks like the face of Apollo

pottery shard or something like that?

pottery shards break differently--cleaner breaks that arc across the curved surface.
If this were made of clay then fired, I would guess it would have a more regular perimeter.
Well-fired clay is very inert and keeps its shape for thousands of years underground.
If it were unfired clay, it would have dissolved into nothing long ago, except in perhaps the driest deserts.
I'm going with Sel's assessment that it's some base-metal alloy, that's been buried and taken on an "earthy" patina over centuries. The face does look Greek style--perhaps Apollo--but I haven't seen one of these.