Just like the main domain on your account, add-on domains have their own email account. Add-on domains do not have their own Control Panel to separately manage their site, the email account must be added through the main control panel.
Here are the steps to add an email account for an add-on domain:
1. Login to 'cPanel' with the URL: yourdomainname.com/cpanel
2. Click 'Email > Emal Account'.
3. Click "create"
3. Enter your email username that you want to use for the email account and click the drop down
icon to select the addon domain name and the last click "create"