You have a Belgian copy of a generically Smith-&-Wesson-style revolver. The Oval-mark-and-letters you note, on the rear face of its cylinder, is a proof-house mark from Liege, Belgium.
While some Browning-designed guns have always been made in Liege, Belgium, none of them are revolvers. To my knowledge, Browning did not design any revolvers.
The "JMB" mark on its grip, underneath the grip panel, could mean absolutely anything, including one-time ownership by John M. Browning. But to connect this gun to Browning, personally, would require a paper trail and a lot of research. It is also possible that this gun was an import, purchased from Browning's shop in Utah; but proving that, too, would require a lot of research and a strong paper trail.
I am not certain that the "3" stamped on the butt of this gun is its serial number. When this pistol was made, there was no specific requirement for a serial number. On the other hand, it may indeed be a serial number, but, without knowing the actual maker of the gun, or its importer into the US, it's impossible to tell.
If you are interested in research, and if you can connect this pistol to either John Browning or to Browning's shop, you will have a very valuable antique gun on your hands. Without those connections, I think that it will prove to be neither particularly interesting nor worth very much.
But I could be wrong.