While you're in Settings, check your Wi-Fi and make sure you're connected to a network you know (or not connected at all and using mobile data).If you're connected to a random network, such as the ubiquitous "public network" (caused by a bug in nearby Windows laptops), that never works.To make sure that your account settings are correct, compare the settings in the Mail app to the settings for your email account: If you have a POP3 email account, then you can only check email on one device at a time.Close other email programs and sign out of webmail sites that you have open. They go to pick up an email and get "This message has not been downloaded from the server" instead.
On the Next Screen, Please make sure that you enable Show All Inboxes as shown in the next image.
Thus, your Inbox will appear to have a set of missing emails. The problem is that IOS Apple Mail hasn't "fetched" those gap emails yet and therefore is not showing them in your other email clients on the face of the planet (including Apple OSX Mail) fetch from your mail server by latest arrivals first instead of most recently copied or moved.
Or fetch them all, which avoids the problem as well.
To check if your email is a POP3 account, go to Settings If your email provider requires your account to use port 25, then you can only send email when you’re connected to your email provider’s network.
Check with your email provider for settings and availability.