Apple mail and Gmail synching issue

I access most of the mail sent to my Gmail address on my iPad, using the Apple Mail app. However, several messages have come in to my iPhone, computer, and Gmail app on the iPad, but they never appeared in my Apple Mail app ( which has always been my main source for emails) on the iPad Air 3. It's updated to the latest IOS, and there are no other problems.

Is there a way to reestablish a reliable connection? I've tried rebooting the device, but that did nothing. I'd appreciate any other ideas. Thanks.