It's probably an older Model 37, Featherlight deerslayer.
Sounds like a winner. My dad gave me his this yr , if its an older model the barrel is smoothbore , like mine , if newer should have a rifled barrel if its a deerslayer. Great gun from what I can tell , I use my H&R for deer , but take this occasionaly for small game. Very light for a 12ga , hence featherlight. Everyone I've spoken to about it says its a quality made firearm. Brand new one will run ya around 700 -800