What type of woodworking clamp is this?
This clamp is one type of a "Hold Down Clamp". Some types are direct bolt on clamps like this one:



Other types similar to the one that you pictured are designed to slip into the flanged head of a pin that pops up through a hole in the work bench.


Here is a picture of one in action where you can clearly see it engaging the pin coming up from the work surface. In this case notice that the work surface has an arrayed set of the attachment points. 



When used on a work surface as shown above this type of clamp has a great advantage of being able to be used rotated around 360 degrees.

Be aware that this type of clamp has has dropped out of favor in more modern times and are hard to find. You could try this link or this link.



The Original Hold Down Clamp (Holdfast), tap with a mallet to set, tap with a mallet to release.