

So, your gun was made between 1908 and early 1911. Can't tell anything closer.
Remington Arms Co. was playing around with this John D. Pedersen designedpump gun for a few years before they offered it to the general public. Here is a 25 May 1907 picture of noted shooter Frank Riehl holding one --

and here is a sketch of a shooter with one in the second 1906 Remington Arms Co. catalogue --
