You need to add some rewrite rules that will examine the sub domain and then rewrite to the relevant path:
<VirtualHost *:80>
ServerName mydomain.com
ServerAlias *.mydomain.com
RewriteEngine On
RewriteCond %{HTTP_HOST} (.*)\.mydomain\.com
RewriteRule ^/(.*)$ /%1/$1
DocumentRoot /var/www/vhosts/mydomain.com/subdomains/subs/www
... more stuff ...
</VirtualHost>
What this will do is capture anything preceding ".mydomain.com" then rewrite it into the URL as %1, $1 will be the requested resource such as index.html
Be aware this might trip you up if www.mydomain.com is a valid domain for your site!