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I brought this on ebay along with a 1940s 3/8 to 9/32 adapter and it is 3h drive but also has the same design plunger to stop the socket from coming off as aero engineers use but it looks like it is some quick release design. I haven't a clue if it snap on or not.

That fits an older pneumatic screwdriver. The long end snaps into the barrel of the pneumatic screwdriver.I assume the other end is 1/4 inch.I don't remember the brand of pneumatic screwdriver.It would be an older one.
The adapter itself is probably Apex brand.They made most of those adapters

Hi there thanks for your reply the big end is 3/8 and the back little square is 1/4 what age would it be? thanks.

I cant remember the brand of pneumatic screwdriver we used a similar piece in.We used it with a bit adapter.But the drive end was same.It was an oddball as most of the drivers took a 1/4 male hex.Age probably 60's ,70's

Hia not been on in a couple of days thanks for your info appreciate it.