Hi there and welcome
Can you tell me please to which email service it is connecting to?
Can you click on my link below please and tell me if you can sign into your account there?
select the mailbox with the issue and click on the Mailbox menu. At the bottom of the pane choose the Rebuild option. If you have a large mailbox, you can expect the process to take a few hours.
Then tell me if they are received please.
yes, either send me a message or rate my service please if it is resolved.
but they also on the server anyway which is why we checked
has the rebuild completed?
Look in the bottom left or right, do you see an error message when it tries to send and receive?
Power off the mac
Then start the Mac and hold down the Command and R keys at startup.
Hold these keys until the Apple logo appears. After your computer finishes starting up, you should see a desktop with an OS X menu bar and an OS X Utilities window
choose Disk Utility from the Utilities window, or from the Installer menu if you're started from an installation disc.
Click the First Aid tab.
Click the disclosure triangle to the left of the hard drive icon to display the names of your hard disk volumes and partitions.
Select your Startup Disk (usually named "Macintosh HD").
Click Repair. Disk Utility checks and repairs the disk.
Let this complete and when it has, tell me if you still have the problem please.
ok, let me know then the results please.