Where does the 0x get stored in memory while storing memory address in a register in a microcontroller
The 0x isn't part of the data and doesn't need to be stored. It is a marker to indicate that the data following the 0x is represented in hexadecimal format. An alternative way of showing hexadecimal data is to follow it with h or H, e.g. 12ABh.

A leading 0 (without the x) can be used to indicate that the following data is represented in octal format (less seen nowadays).

Decimal data is shown without any leading characters.