Please clarify if this a 3 cent piece or a $3 piece.
No such (US) coin exists because the copper-nickel 3 cent piece was not minted until 1865.
Three-cent pieces were minted during the 19th century. If you mean 1873, please see the question "What is the value of an 1873 US 3 cent piece?"
Nickel 3-cent pieces were only struck from 1865 to 1889. If you instead have a silver 3-cent piece with that date, its value would be in the range of $25 to $100 depending on condition.
All 3 cent pieces issued by the US Mint had dates. If yours is worn so the date is not on it anymore then you will have to be know whether it is a silver 3 cent or a nickel 3 cent. The nickel 3 cent is about the size of a dime and the silver 3 cent is smaller than a dime. Without a date the value of these coins would be about $1-$2 for the silver 3 cent and about 25-50 cents for the nickel 3 cent.
It's a common date, worth 3 cents.
Wow! You have a fairly rare coin in your possession - a Silver 3 Cent piece, minted in the year of 1867, in fine condition (F12) is worth: $500.00.The US Treasury also minted in the year of 1867 a Copper-Nickel 3 Cent piece - if this is the coin you possess, its value in fine condition (F12) is: $25.00.
3¢ U.S. FWIW, the coin is just a 2-cent piece. A penny is worth 1¢ so a "2-cent 1-cent" coin would be pretty odd.
It depends on the date, condition and the type. There were two main styles of three cent pieces, there was the 3 cent silver which was tiny and the 3 cent nickel which was large (the 3 cent silver had a star on the obverse, the 3 cent nickel had a head of Liberty on the obverse). Without knowing the date or at least the type, it is impossible to answer your question.
1856 3 cent coin value
In the lower 3 circulated grades that are the most common for this coin retail value is $45.00/$75.00/$105.00 The upper circulated grades are $127.00/$180.00/$216.00
In 1866 both the silver and nickel 3 cent piece were struck. So for the silver in MS-60 $840.00 The nickel is $101.00 in MS-60