To create a custom login screen for the Gnome desktop environment in Linux, you will need to modify the gdm3 configuration files.
First, create a directory to store your custom login screen files. For example, you can create a directory named /usr/share/gnome-shell/theme/my-login-screen:
sudo mkdir -p /usr/share/gnome-shell/theme/my-login-screen
Next, create a file named gnome-shell.css in the directory and add your custom CSS styles to it. For example, you can use the following CSS code to change the background color of the login screen:
#lockDialogGroup {
  background-color: #ff0000;
}
You can also add custom images by placing them in the my-login-screen directory. For example, to use a custom background image, you can add the following line to the gnome-shell.css file:
#lockDialogGroup {
  background: url(background.png);
}
Replace background.png with the name of your image file.
Finally, edit the /etc/gdm3/custom.conf file to point to your custom login screen. Open the file in a text editor:
sudo nano /etc/gdm3/custom.conf
Find the # Uncomment the line below to use your custom theme section, and uncomment the WaylandEnable and GtkLockScreen= lines. Set the value of the GtkLockScreen line .