Hey Krish,
You will need to make sure your HTTPs cert is signed by your internal CA. Or some CA. And that CA must be in STRUSTSSO2, and the browser of who ever is consuming the web service.
as far as the consumer of your web service, you need to find out what ID they are using on the .NET side to make the call to your web service. that ID needs to exist in SU01 and be mapped to the x.509