Is it permissible to deposit and withdraw from the usurious branch of a bank that has two branches (an Islamic one and a usurious one) if the account is with the Islamic branch and the usurious branch is closer?

If money is withdrawn or deposited at the Islamic branch of a bank via the usurious branch, this is permissible. This is not considered assisting the usurious branch in sin, because dealing with usurious banks is not always assisting in sin, just as the Prophet, peace and blessings be upon him, dealt with the Jews who engaged in usury. Overt assistance in sin is that which usurious banks are affected by through their boycott, such as a current account.