The income you receive from NY sources is taxable by NY.
All income you receive from any source in the world (including the NY income) is taxable by PA.
You will need to file a NY non-resident income tax return at the end of the year.
You will also file a PA resident income tax return.
Attach Schedule G-L to your PA income tax return. This will allow you to claim a credit for the tax you paid to NY against the tax you owe PA. Note that the amount of the credit cannot exceed the tax that PA would have charged on the same income. In effect, the combined tax you will be paying PA and NY for your NY wages will be the same as the higher of the two rates.
Since your NY employer won't be deducting any PA state income taxes, you may have to pay quarterly estimated tax payments to PA in order to avoid an underpayment penalty. Remember you have to pay PA tax on all of your other income besides just your wages. You'll need to estimate how much your PA tax for the year will be after deducting the credit for NY taxes on your wages and make the appropriate quarterly payments.
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