Mail not working correctly on iphone 6. Not syncing with Gmail.

Greetings SanjeevGautam,

Thanks for visiting the Apple Support Communities! It seems you're unable to add your Gmail account to your iPhone, as you're receiving an alert that your device isn't connected to the internet.

I suggest restarting your iPhone, and testing with your iPhone connected to a strong Wi-Fi network: Restart your iPhone, iPad, or iPod touch - Apple Support & Connect to Wi-Fi on your iPhone, iPad, or iPod touch - Apple Support

Let me know how it goes from here.

Kind regards.