Login members using web services

I want a login system which authenticate user from web services.The steps should be as follows:

1. we have few member web sites (Outside of wordpress server). Each member website have its corresponding blog which are hosted on different server.

2. We have the web service to fetch the correct authentication from member web sites.

3. I want the functionality so that when someone not logged in member web site and try to access of corresponding blog then he should be redirect to a custom login page.

4. If someone already logged in member web site then he can access the blog.

5. The wp-admin will work as it is. so someone goes to https://www.mysite.com/wp-admin then he can login with their WordPress database credentials.
6. I am trying to create a plugin.