If the letter G is to the left of Washington's portrait, inside a black ring, then that's the Federal Reserve Seal, and the letter corresponds to a specific Fed bank where the bill was printed. G indicates Chicago.
There was never a 1934 G US $10 bill. The highest series letter, which appears by the date, was D. The "G" is almost certainly the letter code for the Chicago Federal Reserve District that distributed the bill; that's not the same as the series letter. Check to see what letter is next to the date. It could be blank or A to D. Then see "What is the value of a 1934 [letter] US 10 dollar bill?" for more information.
No US $20 bill carries a "G" series letter. You may be looking at the Federal Reserve District letter. The series letter, if any, on US bills is next to the date. Regardless, a date is needed in order to estimate a value. Please determine the bill's date and see the question "What is the value of a [date] US 20 dollar bill?" for more information.
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Please post a new question with the bill's date and whether there's a letter next to / under the date.
The 1934 series only extends to the letter D. You may be confusing the Federal Reserve Bank letter with the series letter; that's next to the date, not in the center of the seal. Please see the question "What is the value of a 1934 US 20 dollar bill?"
The serial number and most times the letter on the bill.
Please post a new, separate question with the bill's date and seal color, and provide the letter if any that's next to the date. No US $20 bills ever had a series letter G; you're most likely looking at the Federal Reserve District letter that identifies the district that distributed the bill.
I looked, the back of my five dollar bill isn't red, but thank you for aski g
Please check your bill again. "E" is the highest series letter for 1950 $20 bills. You're probably looking at the Federal Reserve District letter instead; the series letter (if any) is next to the date. When you've identified the series letter, check the question "What is the value of a 1950 [letter] US 20 dollar bill?" for more information.
"E" is the highest series letter for 1928 US 1 dollar silver certificates. The only $1 bills with a G series letter were dated 1935. Please check your bill again and post a new, separate question.
Please check your bill again and post a new, separate question. "G" is the highest series letter for 1928 US $2 bills.
The US didn't print any bills dated 1979 and no $2 bills ever reached a series letter of G. Please check your bill and post a new, separate question.