To take backup of your Emails separately please follow the below steps:
1: Open your C-panel, Click on the "File manager" and go to your "Home Directory".
2: Under Home Directory there are two folders "ETC and MAIL" which contains your all emails data.
3: Right click on folder and compress it and create the zip and you and download that zip as backup of your emails.
Note: To Know how to restore your Emails backup please click here
