What type of shotgun says Riverside Arms Co on the side and Patented August 12th 1913 and 44 Shot on the barrel and what is its value?

The shotgun you are referring to is likely a Riverside Arms Company shotgun, which was produced by the J. Stevens Arms & Tool Company. The "44 Shot" designation typically indicates the gauge of the shotgun. The value of such a firearm can vary widely based on its condition, rarity, and market demand, generally ranging from $100 to $500 or more for well-preserved examples. It's advisable to consult a firearms appraisal expert or a reputable firearms dealer for a more accurate valuation.