Each time I open Emacs it shifts slightly to the right of my screen

I like to have Emacs start dead center of my screen. I am running it on fedora Gnome. Gnome has a setting to center windows. If I start Emacs the 1st time it starts dead center. Thereafter it moves ever so slightly to the right of my screen. It does this a few times before starting in the center again. I would always like it to start in the same place.

Same here on KDE, but I think that's an issue of your desktop manager.

Sadly, modern desktop/user interfaces have decided that only they (and not the applications themselves) get to decide where top-level windows are placed. Wayland actually considers it a security problem that applications might be able to place top-level windows, and forbids it as an explicit policy. There are a fairly large number of places in emacs where it attempts to adapt to/around various desktops/window managers, but this is a slowly losing battle. To get the behavior you want, you can either switch window managers (which is a pretty deep change in some desktops), or figure out how to configure your window manager to DTRT. Asking at the user fora for your particular desktop is probably required, although it’s possible that someone here has experience with your specific combination. This means including the name and version for the window manager used and the desktop system. X11 vs. Wayland is also very relevant, as I implied above. I haven’t used Fedora for a long time, so it’s possible that just saying ‘Gnome’ and a specific version of Fedora is enough. Hope that helps!

Thank you for your helpful comments. They are much appreciated.