XPT2046 (not XTP) is not a LCD display designation, it's just resistive touch screen controller chip, which is used in several different LCD modules. That's why you can't find any distro for it.
You should find some other designation on it, e.g. ILI9341 or something similar.
Or please post images of both sides of your LCD module here.
It looks like this one is another clone of Waveshare 3.5 inch LCD:
They have three different models (A, B, C) with different drivers, but most likely, your one refers to A model.
User manual: https://www.waveshare.com/w/upload/1/1e/RPi_LCD_User_Manual_EN.pdf
Distro: https://drive.google.com/open?id=1xsvANujoImwVQvdf0n7IiUjP8BuCe2GK (could be very old but you can try it at least to check if it would work with your LCD).
If you get no luck with this one - you can try B or even C (least likely) drivers/distros.
About installation and configuration of the driver you can read this thread.