Remington didn't make a 44 pump and I suspect the year is actually a patent date your reading on the barrel which is not the manufactured date. If it's a 22lr with no markings it's probably a model 12. Value is GREATLY determined by condition for which none is supplied.
1912
1912
1912
1912
it depends on the year of the Remington 1100
your 1911 was made in 1912 by Colt or Remington
First year production 1912.
made in 1912 by Colt for US Navy or made by Remington
Saw one for $200 earlier this year
Serials: 162478 - 1912 (probably late in the year based on serial list) 462478 - 1919
Value could range from 100-1000 USD dependingon EXACTLY what it is.
What kind of Remington 22? Also please check my bio page about describing your firearm to get the best estimate on value.