I'm currently using Dedicated server to test my zen cart website.
The temporary url i have been assigned is http://serverip/~username/.

I can access my website but if i click on any category i get server error. The following .htaccess file is for http://www.mydomain.com but here in this case a new folder ~username is compulsory to access the pages.

RewriteEngine On

Don't rewrite any URIs ending with a file extension (ending with .[xxxx])

RewriteCond %{REQUEST_URI} !.[a-zA-Z]{2,4}$

Don't rewrite admin directory

RewriteCond %{REQUEST_URI} !^/admin.* [NC]

Don't rewrite editors directory

RewriteCond %{REQUEST_URI} !^/editors.* [NC]

Don't rewrite cPanel directories

RewriteCond %{REQUEST_URI} !/cpanel.* [NC]
RewriteCond %{REQUEST_URI} !/frontend.* [NC]

Handle all other URIs using Zen Cart (index.php)

RewriteRule (.*) index.php?%{QUERY_STRING} [L]

Please tell me what should be added to access the pages on dedicated server?

I don't know if it will work anyway with an ip address as opposed to using a domain name, but you are missing an important line when using server-based pathways. Because the root is the server and not the domain name you need to have this as your starting point:

Options +FollowSymLinks
RewriteEngine On
RewriteBase /~username/

Vger

I have updated that but still getting the following error:

404 Not Found
The server can not find the requested page:

Well, has your dedicated server got the mod_rewrite.so module enabled in php.ini?

Vger

Yes they are updated but I have come to know that this URI mapping will not work in such a way.

Thanks for your help.