It is The Sportsman, a three-shot gun. The Model 11 was a five-shot gun.
The Remington Sportsman was introduced in 20-gauge in 1930 --

and the 12- and 16-gauge Sportsman were added in 1931.

Your receiver was put in work during July 1935. The three-bird roll stamp was used from their introduction. By 1936 they dropped to the one-bird roll-stamping and dropped the S prefix to the serial number. In 1937 the stopped the separate serial number sequence for The Sportsman and began serial numbering all the receivers in the Model 11 serial number sequence, and putting the one-bird roll-stamping on all the A "Standard" Grade and B "Special" Grade receivers.

A plain barrel 12-gauge with a after market recoil pad is going to to be about $200 in the pawn shops in my area. My 12-gauge Sportsman with a solid rib, the quite scarce Imp. Mod. choke and the original butt plate was $275 out the door a couple of years ago.