Wrong faces are being selected in Maya

 Max3DN on Autodesk forums:

I had the same problem but I managed to fix it. The issue appeared after some faces had been extruded, undoing until before extruding didn't solve it. I had the same issue on another PC a while ago and the issue appeared after extruding if I remember correct (never managed to solve the issue on that PC).

Somewhere else on the internet I read that it could be related to the graphics card driver. I'm running Maya version 2020.4 (student) on a Surface Laptop 3 13.5 inch Intel Core I5 and 8GM RAM on Windows 10 version 2004. So I went to Device Manager and removed the Intel(R) Iris(R) Plus Graphics driver under the 'Display adapters'-section. Out of curiosity I didn't reboot the computer right after removing the driver but booted up Maya instead and did some testing. With the driver removed the issue seemed to be fixed, faces could be selected normally as expected! Then after restarting the computer to reinstall the driver the issue was back.

Here is how I managed to fix the issue:In Maya, go to Windows -> Settings/Preferences -> Preferences.
Select the 'Display'-category.
Under 'Viewport 2.0' change the Rendering Engine to 'DirectX 11'.
Click 'Save' and restart Maya.

Somehow 'DirectX 11' is the only option that fixed this issue for me, all other 'OpenGL'-options did not solve the issue. The other options might work for you, I just tried all of them until the issue was fixed.

Hope this helps!