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.
Blind Date - 1934 was released on: USA: 20 July 1934 (limited) USA: 31 August 1934 (New York City, New York)
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.