SX1 is right. Here's what one source had to say about the Knickerbocker. It also references your "twist steel" barrels:
The American Gun Company was the "house brand" of H&D Folsom Sporting Goods, New York City, c. 1895-1930. The guns were manufactured by Crescent Arms, Norwich, Connecticut.
Their single barrel shotguns sold for less than $10 when new. Their double barrel shotguns sold for $10-$15 when new.
Old trade-name shotguns are not generally collected and not safe with modern ammunition, so are valued solely as a mantle ornament.
The value of these guns if they are broken, badly worn, or rusty is less than $50. In like-new condition, it might be over $200. In "average" condition, it would probably be about $125.
Some people have asked about "genuine Damascus barrels." Before the invention of fluid steel barrels, shotgun barrels were made by winding strips of metal or wires around a mandrel and hammer-welding them. There were several different styles and damascus barrels were the best type of hammer-welded barrels available. In fact, they were better than some inexpensively-made fluid steel. But they cannot withstand the pressures created by smokeless powder and are generally considered unsafe by modern standards.
Here's verbatum from Standard Catalog of Firearms:
"American Gun Co. / Norwich, Connecticut / Crescent Firearms Co - Maker / H & D Folsom Co - Distributor / Side x Side Shotgun "A typical trade gun made around the turn of the century by the Crescent Firearms Co. to be distributed by H & D Folsom. These are sometimes known as 'hardware store guns,' as that is where many were sold. This particular gun was chambered for 12, 16, and 20 gauges and was produced with or without external hammers. The length of the barrels varied, as did the chokes. Some were produced with Damascus barrels; some, with fluid steel. The latter are worth approximately 25% more."