There were a good many commercial riot guns made by Ithaca- some non-US marked 'commercial' trench guns too, though those usually have 7-digit serial numbers. There were 'S prefix' riot guns made for both the US military and the South Vietnamese during the war. There was even a tiny handful of 'S prefix' trench guns.
The listing below might be interesting to look at. I'd be careful of taking any proffered trench gun at face value these days without knowing for sure what you were looking at. Given the prices trench guns and any US marked shotgun might be offered at, there are fakes out there... at minimum, an investment in Bruce Canfield's collector guides to US military shotguns is in order. A lot of homework is too, IMHO.
http://www.gunbroker.com/Auction/ViewItem.aspx?Item=166210420
thaca 37 Trench gun,VERY RARE, slam fire, 1960 era trench gun,this model was manufactured for commerical sales, 12ga, 20" bbl, parkerized, bbl reads Ithaca 37 featherlight cylinder bore, there is an anvil w/ a P inside it on the bbl and the receiver, 2 3/4" chamber, 5 shot, factory heat shield with bayonet lug, front bead sight, walnut wood stock and forend, both in good shape no nicks, sling swivels attached, bore is clean, finish is in good shape there are some scuffs on receiver, takes a 1917 bayonet, not marked US, all original from factory like this, 95% overall, we don't know how many rounds went through it, serial #371120XXX, USED, no local pick up, no credit cards, we are a FFL
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lpl