Why do you think New York is taxing your New Jersey income? Are you looking at "New York taxable income" on line 36 or 37 of Form IT-203? In spite of the wording, that is not the amount of income that you are actually paying New York tax on. The way the tax is calculated is complicated, confusing, and hard to follow.
The first page of New York Form IT-203 has two columns for income. The first column is federal amounts, and the second column is New York amounts. The federal amounts on lines 1 through 19 should be the same as on your federal tax return, and include all your income. The New York column should not include the income that you earned when you were living and working in New Jersey.
The way New York calculates the tax, it first calculates tax on your entire federal income, after New York adjustments. But then it applies an "income percentage" that is your New York income as a percentage of your total income. That's how it adjusts the tax based on how much of your income is taxable by New York.
Lines 38 through 44 calculate what the tax would be if you paid tax on the full New York taxable income.
On line 31 there are two figures for New York adjusted gross income, the federal amount in the first column and the New York amount in the second column. Line 45 calculates the New York amount as a percentage of the federal amount. That's the "income percentage." The hypothetical tax on line 44 (the form calls it "base tax") is then multiplied by that percentage to determine the actual "allocated" tax on line 46.
To take a simplified example, suppose your total federal income is $100,000 and your New York income is $50,000. The income percentage will be 0.5000 (i.e. 50%). If the tax on the full $100,000 "New York taxable income" is $6,000, your actual New York tax will be $6,000 x 0.5000 = $3,000.
