ADD VNC USERS

We will be using user=client2 it will differ in your case. You can use any username for the same.

adduser client2
root@server1:~# adduser client2
Adding user `client2' ...
Adding new group `client2' (1001) ...
Adding new group `client2' (1001) ...
Adding new user `client2' (1001) with group `client2' ...
Creating home directory `/home/client2' ...
Copying files from `/etc/skel' ...

Enter new UNIX password: <--yourpassword
Retype new UNIX password: <--yourpassword
passwd: password updated successfully
Changing the user information for client2
Enter the new value, or press ENTER for the default
    Full Name []: <--ENTER
    Room Number []:<--ENTER 
    Work Phone []:<--ENTER 
    Home Phone []:<--ENTER
    Other []:<--ENTER 
Is the information correct? [Y/n]<--ENTER

Once the client is added

Start the vncserver with the user, for this use:

Then access the desktop by entering the passwords created previously.

su client2
vncserver

You will require a password to access your desktops.

Password:  << enter the password used on the VNC connection
Verify:  << confirm the password

xauth:  file /home/client2/.Xauthority does not exist
xauth: (stdin):1:  bad display name "vps.server.com:3" in "add" command

New 'vps.server.com:3 (client2)' desktop is vps.server.com:3

Creating default startup script /home/client2/.vnc/xstartup
Starting applications specified in /home/client2/.vnc/xstartup
Log file is /home/client2/.vnc/vps.server.com:3.log

As you can see "New 'vps.server.com:3 (client2)' desktop is vps.server.com:3", here ":3" implies the port 5903.

So, Your VNC access port for this user is 5903

client2@vps:/root$ vncserver -kill :3
Killing Xvnc4 process ID 22627
client2@vps:/root$ cd /home/client2/
client2@vps:~$ nano ~/.vnc/xstartup

Make sure it looks like

#!/bin/sh

[ -x /etc/vnc/xstartup ] && exec /etc/vnc/xstartup
[ -r $HOME/.Xresources ] && xrdb $HOME/.Xresources
xsetroot -solid grey
vncconfig -iconic &
x-terminal-emulator -geometry 80x24+10+10 -ls -title "$VNCDESKTOP Desktop" &
x-window-manager &

gnome-panel &
gnome-settings-daemon &
metacity &
nautilus &
client2@vps:~$ vncserver :3
xauth: (stdin):1:  bad display name "vps.server.com:3" in "add" command

New 'vps.server.com:3 (client2)' desktop is vps.server.com:3

Starting applications specified in /home/client2/.vnc/xstartup
Log file is /home/client2/.vnc/vps.server.com:3.log

Now you can VNC into the server using SERVER_IP:5903 for this user.