Enter the W-2 as it was reported.
When you do your state returns, be sure to allocate the proper amount of income to the proper state.
Do your New Jersey Part-year resident return first and allocate the 2 weeks of income earned while living there.
Next do your Part-year resident New York return and allocate the income earned when living in New York.
You should be taxed on 2 weeks of income and get a refund from New Jersey for the extra tax withheld.
You should be taxed on the remaining income on your New York return and will likely owe.
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