If you deposit the check or other form of payment on Saturday in the morning then the payment might be processed the same day.
But if you get to the bank around an hour before closing time on a Saturday then the payment won't be processed until the following Monday.
Payments such as bill payments and Mortgage payments would be processed on regular business days such as Monday through Friday.
Unless you make the payment during the first hour or so of the bank opening.
Or if you make a Payment on say Sunday night then the bank will process the payment sometime Monday when the bank opens.