The only way to find out for sure the 'born on' year of any 870 is to call Remington at 1-800-243-9700 during business hours (NC). Go through the phone tree and talk to a staffer, give them your model number (870) and serial number and they can look it up. There's no posted list anywhere, for whatever reasons.
Some say just use the barrel codes, but there's no guarantee your gun has its original barrel or that the barrel and the gun were made in the same year if it is the original barrel. Go by the serial number if you really want to know.
lpl