New Ticket URL for 3rd Party contact center Screen Pop

Is there a URL or a URL method I can use for a 3rd party contact center that will pop a new ticket window?

I can trigger any URL to open when they receive a call, I just want the users to be able to take information and enter in a user and type out case details. 

I know there are some API for some contact centers, but there is not one for this one.