You should use YourSite.MyDomain.com and not MyDomain.com/YourSite for such a setup.
Just as a sidenote, domains names are always lowercase, if you use uppercae characters, it might cause your sites to not work as paths in linux are case sensitive!
1) Create DNS A-Records for every subdomain e.g. yoursite.yourdomain.com
2) create a website yoursite.yourdomain.com
repeat setps 1 and 2 for each website. If you run your server behind a router, make sure that you use internal ip addresses in the website settings and the external ip address in the dns settings. You should select the IP address and not * in the website settings. If the ip is not listed, add it in the server settings.