SSLv3 is an older security protocol and is generally considered insecure. While it would be highly recommended to make sure your software can use more recent security protocols, sometimes you may need to enable SSLv3 for your host. Please keep in mind that allowing SSLv3 is a security risk and that we would advise against any activity that requires it to be enabled.
Log in to WHM and navigate to the following location:
WHM >> Service Configuration >> Apache Configuruation >> Global Configuration >> SSL/TLS Protocols
You should see a line with "-SSLv3" defined. Change the "-" to a "+" and save the configuration at the bottom of the page. You will then be prompted to restart Apache and to save these new settings.
This can also be updated for Dovecot as well. To update this setting for Dovecot, navigate to "SSL Minimum Protocol" in WHM'S "Mailserver Configuration" (WHM >> Service Configuration >> Mailserver Configuration >> SSL Minimum Protocol). Update the minimum support line to SSLv3 and save at the bottom.
For more information regarding the editing of your cPanel server's security protocols, please see the following documentation: