Support

There are two entirely different things which are both called FTPS: FTP over Implicit SSL and FTP over Explicit SSL.

FTP over Implicit SSL is supported just fine by PHP and, by extension, Akeeba Backup. It means that the FTPS port you're using on your server is different than the plain FTP port and it expects a TLS connection.

FTP over Explicit SSL is properly called FTPES –there's an extra E in there– but it's usually truncated to FTPS by many interfaces, including FileZilla and WinSCP, to the massive confusion of people like you. The difference in this method is that the plain FTP and the encrypted FTPES connections take place on the same port. The client has to connect to the server, negotiate a mutually acceptable encryption method with it and then proceed to establishing an FTPS connection. This method is not supported by PHP, therefore we cannot support it in Akeeba Backup.

For more information please check https://en.wikipedia.org/wiki/FTPS

In order to use FTPS with Akeeba Backup you need:
[*] A remote FTP server which supports FTP over Implicit SSL (FTPS)
[*] Enter the FTPS port in Akeeba Backup (instead of leaving it empty or using the unencrypted FTP port 21)
[*] Your web server, where Akeeba Backup is running, must have an up-to-date version of OpenSSL and PHP must be compiled against it, otherwise no crypto features such as FTPS will be available.
[*] Your web server, where Akeeba Backup is running, and the remote FTPS server must agree on the encryption method to be used.

Unfortunately PHP does not give us any way to figure out if any of these conditions is not met. In all cases it returns the same error message as providing the wrong connection information :(