Selective Backup in Apple Mail Email Client I have an IMAP Gmail account which I have logged in through Apple Mail email client on my Mac book pro. I have sorted out some important emails and made a separate folder for those emails. Is it possible to backup only that email folder and not all the emails along with them? Thanks for your help.
In mail.app, you can select a folder and from the main menu choose ‘Mailbox > Export Mailbox’, select a location for the export file and click ‘choose’.  Mail exports the mailbox as an .mbox package.  

See also this page: https://support.apple.com/kb/PH19174?locale=en_US