Have you copied your public key to your remote ~/.ssh/authorized_keys file and are still being prompted for your password? There’s a good change that the permissions are wrong on that file. If you look at the ssh logs, you can see entries like this:
$ sudo tail /var/log/secure Jun 5 17:27:16 server sshd: Authentication refused: bad ownership or modes for file /home/sean/.ssh/authorized_keys
Change the permissions mode to 600 and you should be able to login as intended.