More information is needed because its value depends a lot on its year and series letter. US Note $2 bills from the 1950s and 1960s are only worth slightly more than face value. Bills from 1928 can be worth over $100.
Among other things make sure that the bill is in fact a United States Note. Those words should be across the top of the front of the bill. Also nearly all common-date US Notes have red seals and serial numbers. Anything dated 1976 or later will have a green seal and is an ordinary Federal Reserve Note with little or no extra value.
Then please post a new and separate question with the bill's date and what letter (if any) is next to the date. You don't need to give its serial number, though.
Could you check your bill again? A red seal would indicate that your bill is a United States Note; the first $2 FRNs were dated 1976 and have green seals. If you have a US Note, there's more information at the question "What is the value of a 1928 US 2 dollar bill?"
Your bill is called a United States Note rather than a promissory note. There were eight different subseries within the 1928 series date; please see the question "What is the value of a 1928 US 2 dollar bill?" for specific information about values.
US $2 Federal Reserve Notes printed since 1976 are generally only worth face value in circulated condition. An uncirculated 2003 note might retail for all of $3.
Please don't assume that every bill is a Federal Reserve Note. The banner across its top and the red seal indicate it's a United States Note, a form of paper money issued directly by the Federal government. US Notes were discontinued in the 1960s. There's more information at the question "What is the value of a 1928 G US 2 dollar bill?".
If the bill is dated 1963 or earlier please look for questions in the form "What is the value of a US 2 dollar bill."If the date is 1976 or later, all the "A" means is that the bill was distributed by the Boston Federal Reserve District. Unless it's in pristine condition, a $2 Federal Reserve Note is worth face value only.
All Series 1953 US $2 bills were printed as red-seal US Notes. Please see the question "What is the value of a 1953 US 2 dollar bill?" for more information.
Could you check your bill again? A red seal would indicate that your bill is a United States Note; the first $2 FRNs were dated 1976 and have green seals. If you have a US Note, there's more information at the question "What is the value of a 1928 US 2 dollar bill?"
Your bill is called a United States Note rather than a promissory note. There were eight different subseries within the 1928 series date; please see the question "What is the value of a 1928 US 2 dollar bill?" for specific information about values.
$3 in average condition, $8 in perfect condition
Please check your bill again and post a new, separate question. The US didn't print any $2 bills with that date.
two dollars
There were no silver certificates dated 1963. The banner across the top of your bill and its red ink indicate that it's a United States Note. Please see the question "What is the value of a 1963 A US 2 dollar bill?" for more information.
That is a US Note, and fairly common. In good condition, they are worth about $2.50.
US $2 Federal Reserve Notes printed since 1976 are generally only worth face value in circulated condition. An uncirculated 2003 note might retail for all of $3.
Please don't assume that every bill is a Federal Reserve Note. The banner across its top and the red seal indicate it's a United States Note, a form of paper money issued directly by the Federal government. US Notes were discontinued in the 1960s. There's more information at the question "What is the value of a 1928 G US 2 dollar bill?".
Please see the question "What is the value of a 1953 C US 2 dollar bill?" for more information. The red seal indicates that it's a United States Note, a form of currency issued until the late 1960s. All 1953 US $2 bills were printed as US Notes.
F3 is almost certainly a plate position indicator, and as such doesn't identify the bill or affect its value. Please see the Related Question for more information about the value of a 1963 $2 US Note.