The New York Arms Co. was in business around 1880-1900, but I have not seen much info on them. They may have been associated with Freeman Hood, who owned or had an interest in several gun companies, including the Hood Firearms Co.
The company is generally associated with the class of revolver called a "suicide special" but evidently they went upscale at some point to produce DA revolvers.
FWIW, the term "automatic", applied to a break top revolver in those days, mean automatic extraction, in other words the cartridges were ejected when the gun was opened rather than having to be poked out with an ejector rod or with a separate rod.
Jim