On W2 form, box 14, it says 414H. Do I put Other at the bottom or NY 414H Tax exempt? My W2 just has 414H.

You should not select Other.  You should select either NY IRC 414H Subject to NY Tax or NY IRC 414H Tax Exempt.  Check the list below - if you are a member of one of those groups and that is the source of your retirement contributions, then you should select Subject to NY Tax.  Otherwise, select Tax Exempt.  

The following 414(h) retirement contributions shown on federal form W-2, Wage and Tax Statement, are taxable by New York State.

Hi. My employer tolder me that the money was already taxed. Do I still select subject to NY tax?

"My employer told me that the money was already taxed."

By this, did your employer mean that the amount of the contribution to the 414(h) plan was included in Wages in Box 1 or had the contributions to the 414(h) been removed from Wages?

To borrow from AnthonyC's answer above:

"

The following 414(h) retirement contributions shown on federal form W-2, Wage and Tax Statement, are taxable by New York State.

• A member of the New York State and Local Retirement systems, which include the New York State Employees' Retirement System and the New York State Police and Fire Retirement System.
• A member of the New York State Teachers' Retirement System.
• An employee of the State or City University of New York who belongs to the Optional Retirement Program.
• A member of the New York City Employees' Retirement System, the New York City Teachers' Retirement System, the New York City Board of Education Retirement System, the New York City Police Pension Fund, or the New York City Fire Department Pension Fund.
• A member of the Manhattan and Bronx Surface Transit Operating Authority (MABSTOA).

"

If your 414(h) contribution is to one of the entities just above, then put it in the category of NY IRC 414H Subject to NY Tax.

Otherwise, put it in the category of NY IRC 414H Tax Exempt.

What a great, helpful answer. Thank you!