Are there jobs that hire 14 year olds in New York?

Answer 1

Farms and newspaper delivery are the two main sources of employment.

https://www.labor.state.ny.us/workerprotection/laborstandards/workprot/wptypes.shtm

Answer 2

Or you could try to do something else.. "Under the table" as some people put it. Mow lawns, pet care, babysitting businesses, etc.
Other than that maybe try your local grocer, some places hire cart pushers, and younger people to help elderly with groceries.