1.Mapping a module to custom domain
Let's suppose you are admin for domain example.com and you want to map subdomain www.example.com to module webmodule in your application myapp.appspot.com
www.example.com -> webmodule.myapp.appspot.com
What you can do is going to admin.google.com and in App Engine Apps section configure your application so that it is mapped on web address www.example.com. Of course follow the instruction for configuring your domain (you should add a CNAME entry in your DNS configuration with ALIAS www and HOST ghs.googlehosted.com).
Once you did this, web address www.example.com is linked to your application default module. For redirecting to webmodule you need to configure application internal routing with dispatch file, as reported here:
https://developers.google.com/appengine/docs/python/modules/routing
In your case what you need is something like this (this is from dispatch.yaml file for Python application):
dispatch:
- url: "www.example.com/*"
module: webmodule
2.Mapping a version to custom domain
Regarding versions, it seems you cannot map an url to a specific module version. What you can probably do is mapping an url including version to a specific module, but this is maybe little bit confusing.