The 44 was made from the late 1800's to WWII. The position of the extractor will help narrow it down, but getting an exact date is not gonna happen with a Stevens.
What caliber is the rifle? Is the extractor at 6 o'clock, or 7 o'clock position? Is it a coil mainspring, or flat mainspring? Coil spring 44's date to after WWI. If it has the Apr 17 '94 patent date, it's after WWI. If it has the Oct 29, '89 patent date, it's pre WWI.
Some calibers date to prior to the introduction of the 44 1/2, as Stevens dropped calibers larger than .32-20 after the 44 1/2 was on the market.
I'm sorry I can't give you a value based on your description, as there are many variables that affect the value of these guns, including finish, triggers, sights, stocks, grip type, etc.
Hope this helps.