How can I login to OneIM website from another mobile application which is not in the same domain?

You could use employee authentication instead. This uses the Person's centralaccount and the dialoguserpassword fields for authentication.

Users don't know their dialoguserpasswords.. All they know is AD user and password.  I think, we should't change the behavior of web authentication method. Normally users login to the web portal with their AD account and this usage will continue. But at the same time, users should be able to login by accessing the web portal from within the mobile application. But in this scenario they are not in the domain in the mobile app. Can we dynamicly change  authentication method according to if user request from mobile app or web browser?  

Users don't know their dialoguserpasswords.. All they know is AD user and password.  I think, we should't change the behavior of web authentication method. Normally users login to the web portal with their AD account and this usage will continue. But at the same time, users should be able to login by accessing the web portal from within the mobile application. But in this scenario they are not in the domain in the mobile app. Can we dynamicly change  authentication method according to if user request from mobile app or web browser?  

From my understanding that is not possible.

You cannot dynamically change the authentication used. But you can configure a fallback if the first "SSO" (in your case AD based authentication) fails.

Dou you mean that "web designer configuratior editor - Web project -  Try single sign-on, use the following module if single sign-on fails:"  Maybe I can set it as Active Directory user account (manual input)

Yes I do.

Thak you all. I will try this.