Looking at the possibilities. There are several Stevens Pocket Rifles, most of them available in .22 caliber with an 18" barrel. Dates of production overlap with the earliest starting in 1872 and latest ending 1916. Company name will only show if it is before or after 1886 ("Arms & Tool" added that year). I think you need to get a copy of Flayderman's Guide to Antique American Firearms and compare your gun to the pictures and descriptions.
Is it a pistol or a pocket rifle? Either way, it would have been made between 1886 and 1916. You can find a fair amount of information about Stevens guns in Flayderman's Guide to Antique American Firearms or The Standard Catalog of Firearms. Flayderman's bibliography will reference other sources of more detailed information.
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