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Value of 1934c $20 bill
No modern US coin or bill has New York State on it. There was a New York quarter issued as part of the State Quarters series, and $1 bills printed for the Federal Reserve District of New York refer to that city. Neither has any extra value.
The value of a 1918 series one dollar bill from the Federal Reserve Bank of New York can vary depending on its condition and rarity. It could be worth anywhere from a few dollars to several hundred dollars to a collector. It is recommended to have the bill evaluated by a currency expert or appraiser for an accurate assessment.
Spitfire - 1934 was released on: USA: 8 March 1934 (New York City, New York) USA: 30 March 1934
Autumn Crocus - 1934 was released on: UK: February 1934 USA: 24 October 1934 (New York City, New York)
Lady by Choice - 1934 was released on: USA: 15 October 1934 USA: 16 November 1934 (New York City, New York)
Such Women Are Dangerous - 1934 was released on: USA: 8 June 1934 (New York City, New York)
Guilty Parents - 1934 was released on: USA: 2 April 1934 (New York City, New York)
The Personality Kid - 1934 was released on: USA: 31 July 1934 (New York City, New York)
Probably about US$800-$1000 for the set, although a bit less if from the New York ("B") or Chicago ("G") Federal Reserve branches.
To untangle things: You have a $20 Federal Reserve Note printed in Washington and distributed by the New York Federal Reserve Bank. The Mint only makes coins, and in any case the Mint has never had a facility in New York City. There's more information at the Related Question.
A 1934 $100 bill from the New York Federal Reserve features a portrait of Benjamin Franklin on the front and an image of Independence Hall on the back. The bill is predominantly green in color and has intricate designs such as scrolls and geometric patterns. It also includes the signatures of the Treasurer of the United States and the Secretary of the Treasury.