I am not getting this error when I tried using psql
What is your OS and version, your version of PostgreSQL (client, if not the same installation as the server), your version of SSL support, and how did you install the client?
I think PostgreSQL doesn't check it, but the ssl library does
Do you mean the psql client(libpq) will not be able to check?
It means the code which does the checking is not in the PostgreSQL source code, but rather in your ssl library, presumably openssl.
It is weird that that message ends up in the server's log file, as it is the client which is doing the rejecting, not the server. So you would think the client would get the details and the server would get the vague conclusion. But it is certainly not the only ssl error reporting oddity I've seen.
Are you saying the client will be able to login but the error will be reported only in the server log?
No, the client fails with the vague 'psql: error: connection to server at "192.168.0.14", port 5432 failed: SSL error: certificate verify failed'. The server log is where the more detailed reason for the failure goes.