I'll sort that out then. I want to know what sort of proof will I receive after getting the insurance?
Your insurance company will issue a proof of insurance in two ways: 1) They will either give you to original NY state Insurance Cards or provide you with acces to your digital electronic NY State Insurance.2) They will send  an electronic notice of insurance coverage  to the DMV.
excellent explanations now I have a question can I pay by mail?
Follow the instructions in your suspension order. Send the bottom of the order along with a certified check, personal check, or money order made payable to the Motor Vehicle Commissioner for the fine