I want to permanently disable SSH password authentication on OS X and use only private keys for ssh remote logins.

To gain more security when remotely logging into my home Mac mini, I thought it would be better to use only private keys to log in instead of using tunneled clear passwords.

To do so, one needs to edit /etc/ssh/sshd_config; note that you will need root privilege for this command.

Port 22
ListenAddress 0.0.0.0
ListenAddress ::

PermitRootLogin no
PasswordAuthentication no
PermitEmptyPasswords no
ChallengeResponseAuthentication no

PubkeyAuthentication yes
AuthorizedKeysFile	.ssh/authorized_keys

References:

How to use SSH keys and disable password authentication