See New Gmail Messages in iOS Notification Center

In addition to alerting you to new messages, the Gmail app for iPhone, iPad, and iPod Touch can collect emails (including sender, subject, and beginning words) in the Notification Center. You can also choose to see emails only in Notification Center and forego the audible alerts or pop-ups on the lock screen.

You also can set up Gmail in iPhone Mail and have it check for new messages periodically, adding them to the Notification Center as it fetches them. Alternatively, you can add Gmail as an Exchange account with push email support.

See New Gmail Messages in the iOS Notification Center

To have new emails coming into your Gmail account listed and previewed in your iPhone or iPad's Notification Center:

Make sure you have the Gmail app and that you're signed into your accounts on it.
Open Settings on your iPhone. Select Notifications, and then find Gmail and tap it.
Make sure the switch next to Allow Notifications is on/green and that the Notification Center setting under the Alerts heading has a blue checkmark underneath it.
Tapping an email in the Notification Center will open the message in the Gmail app.

Additional iOS Notification Tweaks for Gmail

Once you've turned on the notifications, you can adjust a few more settings to get as many -- or as few -- alerts as you want. Here's what you can control.

See Notifications on the Lock Screen and While You're Using Your Phone

To get additional alerts outside of the Notification Center, tap the Lock Screen and Banners options under the Alerts heading. The first setting lets you see incoming Gmail messages without unlocking your iPhone. The second puts a window up on your phone while you're using another app.

Lock Screen and Banners selections in Gmail notification settings

You can also adjust how the banners behave. Tap Banner Style to access two options: Temporary and Permanent. Temporary means that the banners will disappear after a while, and Permanent means that they'll stay on the screen until you tap or swipe them away.

Banner style settings in Gmail notifications

Adjust Sounds and Badges for Gmail Notifications

The Sounds and Badges switches control additional alerts for your notifications in Gmail. "Sounds" plays a tone to alert you to the notification. "Badges" puts a number on the app icon on your home screen.

The Sounds and Badges options on an iPhone

Notifications Settings in the Gmail App

The Gmail app has its own settings for the messages you'll receive alerts for. Here's how to adjust them.

Open the Gmail app.
Tap the More icon (three horizontal lines) in the upper-left corner, and then scroll down and tap Settings.
If you use multiple accounts in the app, tap one you want to configure. On the next screen, select Notifications.

You have three options here. All New Mail sends you everything that arrives. High Priority Only only alerts you of messages that Gmail flags as important. None turns notifications off.
Your changes save automatically.