I am getting employment payments. And 10% taxes are being removed from when I claim each week. If I want to remove taxes from the additional $600 deposited to me separately each week, what form do I s

TurboTax doesn't have a form. You would need to go your unemployment compensation web site for your state to see if you can change the amount of withholding. 

If the check is coming directly from the IRS and not your state's unemployment office then there may be no way to have more withheld from there ... you could increase the withholding from the state check or send in estimated tax payments instead.