No. The NYS Family Tax Relief Credit has been discontinued for 2017 per the following link, https://www.tax.ny.gov/forms/form_number_order_income.htm:
Form number Instructions Form title
IT-114 Discontinued Claim for Family Tax Relief Credit. This form has been discontinued.
General information
The New York State family tax relief credit is available to qualified taxpayers with dependent children under the age of 17. The credit is $350 and is available through tax year 2016. If the credit exceeds your tax for the tax year, the excess credit will be refunded without interest.