Would an unused portion of the retainer fee be given back to after the case? In which account would it go while the case is pending?

I’m in a hybrid agreement, with a flat fee retainer and an additional contingency fee if the case is successful. Would an attorney, put the retainer flat fee I give him, in a client trust account and he would withdraw it as earned or would he put the fee on his own account? Also in New York, is it correct that non refundable retainers are not permitted? Would any unused portion be returned to me at the end of the case?