The HORI Mini for PS4 is a small handheld USB controller that can be read by the USB-A port on the Quadstick. Unfortunately it cannot be used for authentication for the PS4 console.
Its joysticks and buttons follow the same mapping to Quadstick "usb_*" inputs as the DS4.
USB Host DS4 tester is an example configuration spreadsheet that can be used to base a custom configuration on.