Failed root login attempts on my Linode

This is pretty standard behavior on a server that has not been appropriately secured. It is most often caused by automated scripting and its not generally an direct attack on your server. There are a few ways to prevent this:

• Disable Root Login via SSH and use Key-Pair Authentication.

• Configure fail2ban which blocks multiple login attempts

• Configure your firewall to block connections from unknown IP addresses. I'd recommend reviewing our guide for Centos - Firewalld or Debian - Ubuntu - UFW depending on your distro.

Of all the options, disabling the root password authentication is likely the easiest and I'd suggest doing that first.