New York does not tax your NJ income.  Since you are a NJ resident, New York will only tax the income you actually earned in NY.  However, it will factor in all of your income while determining the amount of NY tax you will have to pay.  NY uses the following formula:  figure out how much tax you would have paid on all of your income if it were all earned in NY, and then prorate that amount to the percentage of income you actually earned in New York.  

If, in your example, your NY income is 50% of your total income, and your NY tax on all of your income were 2,200, then your NY tax would be 1,100, 50%  of the NY tax amount.