If there were local taxes withheld you can file an amended 2016 NJ state return to claim the credit only for local taxes, not state taxes withheld (No PA state taxes should be withheld).
The Reciprocal Personal Income Tax Agreement between Pennsylvania and New Jersey means compensation paid to New Jersey residents employed in Pennsylvania is not subject to Pennsylvania income tax. Therefore, you cannot claim a credit on Schedule A for taxes paid to Pennsylvania on those earnings. New Jersey residents can claim a credit for taxes paid to Pennsylvania on other types of income (for example, business income) that are taxable in both states by completing Schedule A.
The New Jersey/Pennsylvania Reciprocal Agreement does not apply to income or wage tax imposed and collected by the City of Philadelphia or any other municipality in Pennsylvania. That means a New Jersey resident who works in Philadelphia and pays city wage taxes can claim a credit for the taxes paid to Philadelphia.
Do note there will NOT be a full refund as PA and NJ taxes are computed differently and you only get a credit on double taxed income.
To amend a NJ state return. see comment link.
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