Not sure what you mean by unidentifiable or mystery. Braunsdorf-Mueller is a very well-known early tool mfgr, this thread is full of their tools, and you have correctly identified the tool you have found as an offset screwdriver. Just to qualify and clarify what
@RTM means...., there are no known BMCo catalogs in the public space, so we have limited references for them. They are listed as an OEM for many tools, including screwdrivers, in several directory-type trade magazines. But not offset screwdrivers, per se.
Is that a ratcheting offset screwdriver? Is that a gear I see in the head? And is the bit removable?