If I’m understanding your question correctly, you received a lump sum, one-time signing bonus while you were a Pennsylvania resident and are not being paid in installments.
If you received a one-time payment, claim a credit on your part-year Pennsylvania tax return for the tax paid on the whole bonus amount since you were a PA resident when received the bonus.
Your bonus is also taxable to New York even though you were not working in NY because it is connected to NY employment.
On the PA other state credit form (Schedule G-L), you’ll have to calculate the NY tax amount since your NY return will include the total tax on your entire NY income. For example, if your bonus was $10k and your total NY income was $100k, you would report $10k as double-taxed income and 10% ($10k/$100k) of your NY tax liability (IT-203 line 50) as tax paid on double-taxed income.
There is no credit on your New York tax return because you claimed the credit on PA and the rest of your income was earned while living and working in NY. File a part-year NY tax return.
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