When selecting Bills to Pay, and entering a Cheque Date, the date on the posted cheque is not the date specified.
This will be because the field on the Bill itself "Recommended to Pay on" is the default Payment date for the Bill, and will default as the payment date. Check the Bill for the 'Recommended to Pay on' date:
To override this setting, run the Pay Bills function and then on the far right of the screen next to this bill, click on 'More' and then change the Payment Date here. Once saved, you should be able to process a normal payment (with your desired date) for this bill.