In Windows 10 the new action center display notifications from all apps, including the Mail app. Whenever you get a new email, the Mail app will send out a desktop notification and lists the new email in the Action Center.
If you get a lot of emails, the notifications can be rather annoying. If you added multiple emails accounts and you would like receive new email notifications from an specific account you can change the settings to do just that.
1. Open the Mail app. Click the Gear icon on the bottom to open the Settings right pane.
2. Here select Notifications.
3. If you want to turn off email notifications in the Action Center for an specific email account, select the account from the drop-down menu and then turn or off Show notifications in the Action Center. If you would like to turn off notifications to all accounts, select Apply to all accounts.
If you change your mind, you can always come back and turn on new Mail notification banner & sound.