What is the legal age a child can be left home alone overnight by a parent in New York state& parent leaves state for a few days

I don't know. Try calling a hotline or CPS ( child protective services) for an answer. I don't know if different states have different laws.
You didn't mention the age of the child you are talking about.

Here in KY for a child to be left alone for a few hours its 12, to babysit others and be left alone over night its 16.