You need to pass the cookie value to Target as a custom parameter. Using the targetPageParams() function is a great way to do this for a client-side at.js implementation of Target. Then you can setup an audience rule that checks against the custom parameter you are passing into Target.
@aem-explorer If you're going to deliver Experience via Custom Code then inside custom code you can put condition to check cookie value and based on cookie value you can deliver the content. If you're going to Deliver Experience via VEC composer then pass the cookie value as MBOX parameter and then using that MBOX parameter you can able to create the New Audience.