If you're trying to use a USB serial adapter as your Linux kernel console...
The kernel needs to be compiled with CONFIG_USB_SERIAL_SERIAL=y
Debian kernels do not appear to be. Somewhat strangely, the config option doesn't even wind up in the config file in the typical commented-out manner, so you don't even know the option exists until you discover it from random Web searching, and then looking at drivers/usb/serial/Kconfig in the kernel source.
Console drivers need to be built-in, so CONFIG_USB_SERIAL_CONSOLE depends on CONFIG_USB_SERIAL=y. We build the USB serial code as a module so CONFIG_USB_SERIAL_CONSOLE is not an available option. This is unlikely to change, as a built-in feature takes memory from every Debian GNU/Linux installation.