I'm assuming you drive to Pennsylvania and then do local deliveries in that state. In that case, your income would be taxable there. If so, you wouldn't be exempt from Pennsylvania tax withholding, so you should ask your employer for clarification on that. If you drive professionally in more than one state, your income is typically taxed only in the state you live in, but it doesn't sound like that is what is happening here, perhaps you can clarify that for us?
You would need to file a non-resident tax return for Pennsylvania to report the income you earned there. You also need to file a New York resident tax return since you live there. New York will tax you initially on your income earned in Pennsylvania, but you will get a credit on your New York tax for the portion of your income earned out of state. Pennsylvania will give you a credit for taxes paid in New York on your Pennsylvania income. You should prepare your Pennsylvania tax return first and look for a credit for taxes paid to another state and complete that section. When you prepare you New York return, you will be asked to enter the income you earned out of state.
{Edited 3/18/24 at 4:50 PM PST} @Harryo552
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