Android's Gmail application comes with automatic notification settings that alert you as soon as a new email or message reaches your account. If you find these notifications to be irritating, here is a quick way to disable those notifications on your Android phone.
Change Notification Settings on Android's Gmail App
Open your Gmail app and tap on the Menu key (3 horizontal bars at the top left corner). Scroll to Settings:
Next, tap on your email account:
Click on the Inbox sound & vibrate option. This will allow you to customize your notifications:
Uncheck the Notifications checkbox to disable any notifications from your Gmail app. Your new settings should be automatically saved: