I would say 1930’s on the badge as well. TWS does stand for township. My great great Uncle was the Alma Town Marshall killed by Buck Barrow, and W.D. Jones, and his badge is very similar to yours. Policing wasn’t as far as advanced as it is today, there was no “mass” suppliers of police wear, so they would order the blank badges out of a catalogue, or newspaper. Depending on the size of the city there may have been one or multiple constables or marshals. They all operate under the direction of the sheriffs office since the county seat back then(county courthouse), would be the ones who they took their inmates to, since most towns only had a simple office, and maybe one cell. In our neighboring city, they had one marshal as well, and the arrested individuals had to be put in a concrete building approximately 8x8, with iron barred windows, and a heavy solid iron door. I’ll get pictures of it later. It just snowed here so it’ll be hard to get to, but it gives you the idea about which the police, marshals, Constable, and deputies had to deal with, and what they used back then.