If this is basically a copy of a Colt Police Positive it is most likely a Cosmopolite Oscillatore made by Garate, Anitua y Cia of Eibar. Made from 1925-33 though my reference says it is in .32 Long Colt. The main visual difference between it and the Colt is the the ejector yoke is unlatched by pulling the ejector-rod forward. Also made in .38 Long Colt.
The only other plausible listing I could find by Garate is the L'Eclair; a five-shot 8mm Lebel. Though I doubt it's this model.
The .32/20 has me stumped though, especially the tag on the barrel. Is the barrel marking in the same script as any other markings? Possibly it was added later for marketing purposes. On many of these older "suicide specials" the marketing department would put any Madison Avenue company to shame. There wasn't even a vestige of truth in much of the advertising back then in any retailing of any sort, not just firearms.