If you work in New York and live in New Jersey you definitely have to have New York tax withheld from your pay. You will pay New York tax on all the income you earn for working in New York.
You probably do not need to have any New Jersey tax withheld from your pay. You have to report the New York income on your New Jersey tax return, but since New York tax rates are higher than New Jersey, the credit on your New Jersey tax return for the tax you pay to New York will eliminate any New Jersey tax on your income from New York. If the income from New York is your only income, you will not have to pay any New Jersey tax. The only reason you might want to have New Jersey tax withheld is if you have other income that is taxable by New Jersey but for which there is no withholding, such as investment income.
A New York employer that has no employees or operations in New Jersey usually will not withhold New Jersey tax.
If you work in New York and live in New Jersey you definitely have to have New York tax withheld from your pay. You will pay New York tax on all the income you earn for working in New York.
You probably do not need to have any New Jersey tax withheld from your pay. You have to report the New York income on your New Jersey tax return, but since New York tax rates are higher than New Jersey, the credit on your New Jersey tax return for the tax you pay to New York will eliminate any New Jersey tax on your income from New York. If the income from New York is your only income, you will not have to pay any New Jersey tax. The only reason you might want to have New Jersey tax withheld is if you have other income that is taxable by New Jersey but for which there is no withholding, such as investment income.
A New York employer that has no employees or operations in New Jersey usually will not withhold New Jersey tax.
If you work in New York, your employer is required to withhold New York taxes from your pay.
"New York State personal income tax must be deducted and withheld on wages paid to New York State nonresident employees for services performed in New York State."
Section 3(I), https://www.tax.ny.gov/forms/publications/wt/nys50.htm