Note: I have tested this in Ubuntu 18.04 but this works in Ubuntu 20.04 as well.
First disable the default screenshot shortcut from settings:
Create a custom keyboard shortcut in the settings:
Name it gnome-screenshot, put the command as gnome-screenshot as well
Shortcut value : enter the key [Print Screen]
Create a custom shortcut:
Now enter into dconf-editor (Install it if you do not have it yet). Go to: org → gnome → gnome-screenshot → auto-save-directory: Change the auto save directory’s custom value to the one you want.
Enter the custom path:
If this doesn’t work, it’s possibly because you have a different version of Gnome. Either way, whether it works or not, I’m out of ideas.