Tough one.
The reverse design with that small cross reminds me the tiny roman bronzes from their final century, or the small early byzantines.
Looked on these two places which are the most obvious to look on, and found nothing. And most of these have the obverse portrait looking right, yours is looking left. A strange portrait for a roman coin I have to say. Also tried Wildwinds, the woman portraits from Arcadius onwards, nothing too.
Also tried a wider search at Numista of ancient non-precious coins with the size range 8-12 mm and the weight range 0.5-1 g, nothing too.
We have a mystery here.