How can I request refund on an Apple Music subscription?

All you can do is try by going here:

Request a refund for apps or content that you bought from Apple - Apple Support

First time users are given a Free Trial to see if they like the service before being charged. If you do not cancel during this Free Trial, then it is unlikely you would get a refund. In some cases though, Apple may provide a compassionate refund, so give it a shot.