What is the value of a 1963 US 2 dollar bill?

The bill's red ink and the banner across its front indicate that you have a United States Note, a form of currency that was issued until the late 1960s but is now obsolete.

There are two versions of the 1963 $2 bill each with a different secretary name, in uncirculated condition, they are worth;

Henry H. Fowler. $10.00

Joseph W. Barr. $13.00

At any quality other than uncirculated, they are worth face value ($2).

Serial numbersA bill's serial number is a counter and security feature so including it in a question generally doesn't help to identify it or affect its value. There are collectors who will pay a premium for bills with low or patterned serial numbers; e.g.12345678 or 00000005.