Small pottery vessel with what seems to be archeological marks

Hoping someone may know when or where this might be from? Picked up at an estate sale a month or so ago. I’ve been picking up very old/ancient stuff when I can get it inexpensively. I love to look at it! I know a lot is not necessarily rare or valuable but I dig it.

Former owner was a judge who had some connection to China. He had a good sized collection and the vast majority of it was Chinese. I purchased a small supposedly Chinese Song Dynasty vase/vessel at the same sale. That piece was supposed to have been sold as excess inventory by a museum in the Philippines. I’ll have to do more digging on that at some point. Considering the above my instinct would be to guess this is also Chinese but I have no earthly idea. Can anyone here begin to take a stab?

It’s not more than 3” tall or wide

Possible inkwell?