City Ledger payment type won’t show up on the screen if the process starts with the payment list when trying to close the payment as City Ledger aka current on the cash register screen. The reason is that this isn’t a physical payment type.
If you start the current check closing process by clicking the check out button instead of with the payment list, the payment list that comes up on the screen contains the City Ledger payment type.
Note: The process is performed using Check Out if the guest checks out today and using Settlement on the following days.