How do I get a refund for an accidentally charged subscription?

All you can do is try:

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

When you start a free trial, you must double click the side button with the trial period showing on the screen along with the subscription start date and price. There is also a message that says to avoid the charge, you must cancel at least 24 hours before the trial period ends. That is what you agree to when starting the free trial.

In most cases all transactions in the App Store are final due to the explicit actions that need to be taken to authorize them, but at times Apple may provide a compassionate refund. It should never be expected though. When starting a free trial, I always recommend to set a Reminder to cancel at least 24 hours before the end date so I do not forget.

If. you have cancelled, you will not be billed again. However, it's unlikely that you would be refunded the current subscription. You can always visit support.apple.com/billing