For any subscription managed by Apple, you can cancel it here:
If you want to cancel a subscription from Apple - Apple Support
You can try to request a refund here, in some cases Apple will provide a compassionate refund, but normally all transactions are final in the App Store.
Request a refund for apps or content that you bought from Apple - Apple Support
There is no such thing as a free subscription. Some apps will offer a Free Trial that will need to be cancelled at least 24 hours before the trial period ends to avoid being charged. The subscription charges will continue until you cancel it. Did you sign up for the Free Trial in the app where you were required to double click the side button? In that case, the subscription charges and trial period would have been on the screen when you did that.