Refund

As long as you didn't cancel the subscription you had it available, and I would expect you wouldn't be due for a refund. But why are you asking us? This is a user to user forum: you are not talking to Apple here, and refunds are not in our gift. Contact Support using the link I already gave you.

If you don't want to use Apple Music you should cancel the subscription. Please see Manage your Apple Music subscription - Apple Support

Just not using it is very unlikely to be accepted as a reason for a refund, but you could try asking: please be aware that Apple are under absolutely no obligation to refund you.

iTunes Store - Contact Us - Apple Support