It's a German "pocket bulldog" revolver, but I don't recognize a make matching "B&A"; this example has an external safety that blocks the lockwork (the lever on the left side of the frame), and is missing the original ejector-rod, which would have been kept stored in the front of the cylinder pin.
Edit: found it; "B&A" stands for "Bolte & Anschutz", of Zella-Mehlis, Germany.