To disable the notifications in mail, do the following:

1, Go to the Windows Start, and look for the Windows 10 Mail app, and click to open it.

2. Click on the gear in the bottom of the left pane"



3.  To the right of the screen a menu will appear, select "Notifications."




4.  Check the "Apply to all accounts," and then click on the "Off" for "Show notifications in the action center."