Hi Plushboy,
Welcome to Apple Support Communities. We understand that you're having an issue with receiving mail on your MacBook Air but have no issues with receiving them on your iPhone. We'd like to help.
Have you ever been able to successfully receive and load the emails on this device? Do you receive any error messages when you try to open or access these emails? If so, what does it say.
Since the issue is related to receiving emails, this resource may be helpful: If you can’t receive emails in Mail on Mac - Apple Support
If you can’t receive emails in Mail on Mac
In the Mail app
on your Mac, if you’re certain you’re not receiving messages, even after clicking the Get Mail button
in the Mail toolbar, try these suggestions.
1. Check whether Mail is retrieving a large message or a message with large attachments. See View Mail activity.
2. Check if you’re using filters in the message list that are preventing expected messages from being shown.
3. Try sorting messages in the message list by Date or another attribute, or searching for messages, to verify if you received them.
4. Check whether your account is offline or disabled (inactive).
5. If you’re missing emails from a specific person or group, check whether you blocked messages from them.
6. Try quitting Mail, then opening it again.
7. Choose Window > Connection Doctor, then follow any instructions in the Details column. Check for problems logging in to email accounts or with the incoming Mail server, or with firewall software blocking network traffic.
8. Check whether you’re affected by another firewall, such as software installed separately from macOS or built into an internet sharing router, or administered by your email account provider. Contact the appropriate person for information.
9. If you’re still having problems, contact your email account provider to verify your user name, password, incoming mail server, and other required information. Then verify the information is entered correctly in Mail account settings.
Let us know how that goes.
Cheers!