If you want to show payment methods other than the ones offered by Prestashop by default then Custom Payment Method by FME Modules is all you need. Custom Payment Method enables you to give your customers options for multiple payment methods.

Admin can add as many payment methods as they want with very simple settings. You can add a payment method by inputting its name, description, and icons. You can also select the order status for the custom payment method, each time user selects this payment option, the selected order status will be automatically updated.

Prestashop Custom Payment Method Module also allows you to show each new payment method to a specific customer group. While creating a payment option there is an option to select the customers groups for this payment method.