If you are setting up SSH public key authentication in a new Fedora/CentOS install, you must make sure the SELINX configuration is setup correctly for the /root/.ssh folder on the server.
The ~.ssh/ folder is not created on a new install. If you manually create the folder, set the SELINUX permissions with this command:
restorecon -R -v /root/.ssh
Another tip: If you are using the PuTTY Key generator to generate the public key, make sure you copy and paste the text into a single line in the /root/.ssh/authorized_keys file. Each line of the authorized_keys file should have the following: ssh-rsa (key contents) imported-openssh-key