Several different bills could fit that description. Please post a new, separate question with your bill's denomination and seal color.
the serial number does not match the series
Please check your bill again and post a new, separate question. "G" is the highest series letter for 1928 US $2 bills.
Please check your bill again. There were no series letters on 1928 $1 United States Notes. The only 1928 G bills were $2 US Notes.
"F" is the highest series letter for 1928 $5 red-seal notes. Please check your bill again and see the question "What is the value of a 1928 US 5 dollar bill with a red seal?" for more information.
There were no $2 bills dated 1929. However, letters for the 1928 series go up to G so if that's what you have, please see the question "What is the value of a 1928 G 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.
Please check your bill again and post a new, separate question. 1928 $1 US Notes were only issued in one series so there are no subseries letters.
Please check your bill again and post a new, separate question. 1928 red-seal $1 bills don't have series letters.
Please check your bill again and post a new, separate question. 1928 red-seal $1 bills don't have series letters.
"F" is the highest series letter for 1928 United States Notes. Please check your bill again and post a new, separate question.
Please check your bill again and post a new, separate question. There were no series letters on 1928 $20 gold certificates.
You didn't provide a denomination but the only 1928-series bill that was issued long enough to reach F (the small letter next to the date) was the $5 US Note. Please see the Related Question for more information.