Depends on the model but something like a rolling block #1 would be from 1868-1888.
It all depends on the age, condition and the collect ability of the rifle.
This rifle was made in 1920.
I received a similar rifle from my grandfather. He had a letter from Remington stating the rifle was manufactured between 1900 - 1907, if I remember correctly.
1932-1935 - see Remington Society link
106351
In order to determine the exact value of a Remington Rolling Block rifle, a few different factors would need to be taken into consideration. Some of these things would be the age and condition of the rifle.
Date code on barrel, check Remington Society of America - manufactured date link.
1914
Introduction Year: 1948 Year Discontinued:1970
They only made the from 1936 to 1941, really only 1939.
Well there's not a lot of information here to understand what exactly your asking but if it's E. Remington and sons it has to be prior to 1888 when it then became Remington Arms Co.
E. Remington and Sons (predecessor to Remington Arms Co) manufactured firearms in Ilion, New York, from 1860 to 1888.