sync e-mail from macbook to iphone

You should have Mac mail set up to access the Exchange server, and also mail on the phone accessing the same account on the server. The server should be sending mail to both the Mac and the phone, and any action you take such as deleting or moving to a folder on one device should sync back to the server, then the server should sync the action to the other device. If this is not happening it is a server problem. Contact your Exchange administrator.

One thing to try is to delete the account from each device, then add it back.

Email messages never sync directly between devices. Instead each device syncs independently to the email server. If the account is an IMAP or MS Exchange account this will happen automatically if the account is set up correctly. POP accounts do not sync; instead each device manages email independently.

What kind of account is it (e.g., gmail, AOL, yahoo, icloud, Outlook, etc)?