App Mail - update mails

If you have added just now then please give it some time to sync and download all mails.

Also please check if you have added any filter. As shown below

Set up filters to find emails

Use filters to help you find emails that you want to read and hide the rest. You can filter email messages by unread, flagged, email addressed to you, messages from VIPs, and more. Here's how:

1. Open Mail. 
2. Go to the mailbox you want to filter, and tap  in the lower-left corner of your Inbox.
3. Tap Filtered by: Unread, then choose what you want to see in your Inbox.
4. Tap Done.

• To turn off the filter, tap .

Also search for an email

Use search to quickly find an email. You can use Suggested Searches to quickly narrow your results. Or you can search by timeframe — for example, enter February, then tap February under the Dates category to see email from February. 

To search for an email:

1. Open Mail and scroll to the top of the Inbox to find the search field.
2. Tap the search field, then enter what you're looking for. To search multiple accounts, tap All Mailboxes.
3. If you don’t see the email that you’re looking for in the list of suggestions, tap the magnifying glass under the Search field.

To return to your Inbox, tap Cancel.