Because your share is 1/3 as beneficiary, only 1/3 of the distribution is eligible for exclusion. See If you receive pension and annuity income of a deceased individual on page 14 of NY Pub 36:
https://www.tax.ny.gov/pdf/publications/income/pub36.pdf
I don't have TurboTax's NY state software, so I don't know how this is accomplished in TurboTax, but I certainly would not select "Not eligible for exclusion for those over 59 1/2" because a portion of the distribution is excludible from NY state income based on the information in NY Pub 36.
Also see the details on page 13 of Pub 36 regarding distributions from IRAs.
