Is there somewhere to include the information on this account?
You will only report what is on your W-2. A 457(b) is listed in box 12 code G.
Please see the following TurboTax FAQ for additional information.
https://ttlc.intuit.com/replies/3300234
I don't believe NYS return is correct the 457 $20,000 should not be taxed income, what can be done?
The 457 can be pre-tax or after tax dollars. If you chose to do the ROTH version, the income would be taxable. See Public Sector Plan Types - New York State Deferred.
Federal and NY both exempt the retirement income from tax when being deferred as pre-tax.