The commands below will allow configuring password-less SSH access from one Linux server to another using a private key.

Generate SSH Key from client computer. By default, ssh-keygen will create a 2048-bit RSA key pair. It is secure enough for most scenarios. You may optionally pass in the -b 4096 flag to create a larger 4096-bit key.

ssh-keygen

After entering the command, you should see the following prompt:

Generating public/private rsa key pair.
Enter file in which to save the key (/your_home/.ssh/id_rsa):
Press ENTER to save the key pair into the .ssh/ subdirectory in your home directory, or specify an alternate path.
Enter passphrase (empty for no passphrase):

Once key creation is successful, you will see similar output like one below. It will create both private and public (.pub) key.

Your identification has been saved in /your_home/.ssh/id_rsa.
Your public key has been saved in /your_home/.ssh/id_rsa.pub.
The key fingerprint is:
a7:85:24:5b:5e:21:56:b6:d1:e4:2a:44:34:b5:e7:24 username@remote_host
The key's randomart image is:
+--[ RSA 2048]----+
|     ..o         |
|   E o= .        |
|    o. o         |
|        ..       |
|      ..S        |
|     o o.        |
|   =o.+.         |
|. =++..          |
|o=++.            |
+-----------------+

Copy the SSH key (.pub) to the server you wish to access password-less.

ssh-copy-id -i /path/to_file/ssh_key.pub root@YOUR_SERVER_IP

Try

ssh 'root@YOUR_SERVER_IP'