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To fix your Gmail account on an iPhone, verify your internet connection, restart your iPhone and the Gmail app, update the Gmail app or iOS, and make sure your Google account settings (such as IMAP and Background App Refresh) are accurate.  If those procedures fail, try removing and re-adding your Gmail account in your iPhone's Settings or reinstalling the Gmail app from the App Store.

Check the basic settings and connections.

How to Fix Gmail Account on iPhone