Updated: Dec 15, 2022
I suppose all discussions of LEO badges of the old west will have to include consideration of real or fake. Not my concern though, I've only accumulated what little I know about the subject by way of encountering LEOs' badges while researching their gunleather; see above.
Of course near and dear, are Tom Threepersons' badges because of his famed holster. Below the badge held by a private collector as Tom's, and below that image one showing what it should have looked like. Made by L.A. Rubber Stamp that operated 1885 to 1935.
Read more in my book titled "Holstory -- Gunleather of the Twentieth Century -- the Second Edition" that is available at www.holstory.com and printed for you/shipped to you in USA.