It is a server / client TCP communication, I'll use by port of SSL although the TLS should also work. Our server should only accept connections from our trusted client of devices, so I should use the client certificates.
Could you elaborate in what circumstance that is possible "if the server accepts anonymous connections"? The server does not know who requests a connection from the SSL port, but the server will accept the connections if the client certificate and key are valid. I thought as long as the SSL is used, the server can only accept trusted connections, so I am not quite understand if the server could accepts an untrusted anonymous connections.