You owe NY state a non-resident tax return that reports and pays tax on your NY-source income only.  Then on your MA return, you get a credit for out of state taxes that you pay which reduces (mostly) the impact of double taxation.  In Turbotax, prepare the NY return first, then the MA, so the credit flows in the correct direction.  You would need to make NY estimated payments for the NY taxable income.  6% is fairly typical, it could be less for small jobs.  Here is a link.  You can make the payment by check or online. https://tax.ny.gov/pit/estimated_tax/default.htm

If you are hiring a subcontractor, it doesn't really matter tax-wise where they are located.  If you hired the subcontractor to work on your NY-source job, it's an expense on your NY return even if they are located elsewhere.