What is the value of an 1861 US nickel?

The first nickels were minted in 1866.

Prior to that time 5-cent coins were smaller, made from silver, and called half-dimes. If you have a coin that says HALF DIME on the back, an 1861 coin in good condition (G4) is worth $20.00; if it's mint state is MS60, the value is: $200.00.

If it looks like a regular nickel, you are probably looking at a 1981 nickel from the wrong angle. (1981 upside-down is 1861)
The US Mint did not produce a nickel in 1861.