How to get a refund for a duplicate Apple TV subscription?

• You can’t have two of the same subscription on one Apple Account. Apple’s administration prevents that. If you applied a different Apple Account (not advised), then that would count as two totally different users to Apple.
• For service providers that offer an Apple TV subscription as a perk, you still have to activate that as end-user. It isn’t automatic. If you didn’t activate that (when you could), and didn’t supply an Apple Account to link it to, then there is nothing to recoup over that period anyway, as the perk wasn’t active. Often, the offered perk subscription will pause the payments of the direct subscription, while the perk lasts, so that it is seamless and doesn’t need cancelation. See the details in the terms and conditions.
• Getting refunds is time-limited, so while you might be eligible to recoup some of the costs, it may not be all of it. It depends on the exact dates.
• Not ending subscriptions that you don’t want to continue, may not qualify for refunds, as the subscription is for provided access to a service, not for usage of that service per se.
• All refunds are decided on by Apple’s refund staff. Clear user motivation/​explanation counts. I don’t think there is an appeals process (outside of courts).

if it was me then I would try

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

and or reach out to their official support channels

Get Support (apple.com)

And or

Contact - Official Apple Support

And or

https://www.apple.com/contact/

Or

Genius Bar Reservation and Apple Support Options - Apple