This can happen for a few reasons. One is that you have not added the key as an authorized key for that user.
If you added a Public and Private key pair when you provisioned the droplet you can copy the
/root/authorized_keys file to the users
~/.ssh directory with the commends below (as root)
cp /root/authorized_keys /home/USERNAME/.ssh
chown -R USERNAME:USERNAME /home/USERNAME/.ssh/*
chmod -R 0600 /home/USERNAME/.ssh/*
The above commands copy the authorized_keys file to your users home/.ssh directory and sets the user/group ownership and file permissions. REPLACE USERNAME WITH YOUR USERNAME
Another reason is your system has to many keys loaded and is failing due to multiple authorization failures. Try:
ssh -i ~/.ssh/private_key USERNAME@IP/HOST
Please keep in mind the key pair needs to match as an authorized pair for this user as noted above.