oh yes i see it. you need to uncomment the line “PasswordAuthentication no” (this means you need to delete the # in front of it)
the hashtag makes it ignore this option and use default values(which in this case means “yes”).
change:
#PasswordAuthentication no
to:
PasswordAuthentication no
then restart ssh:
sudo service ssh restart
and your ssh error should go away.
i also recommend creating a custom user on your droplet and UNsetting the root password. (but thats only my opinion, other people might have a different view)
create user:
adduser yourusername
add this user to sudo group (for sudo based root permissions, so you can use your userpassword to get elevated/root permissions)
gpasswd -a yourusername sudo
unset root passwd:
passwd -d root
here is a neat article about those steps: https://www.digitalocean.com/community/tutorials/initial-server-setup-with-ubuntu-14-04
i hope this helps, cheers!