How do I cancel a purchase made by mistake?

The Free Trial should appear in the subscriptions if you follow the steps here: https://support.apple.com/HT202039

If its not there, then nothing was activated, so nothing to cancel, and nothing that would charge you.

There's no way to cancel it if it does not show up in the Apple ID subscriptions, since that would technically mean there is nothing that can be cancelled.

Follow the steps here: View, change, or cancel your subscriptions - Apple Support

What app is it exactly?

In general Apps with trials are free to download so would not have any purchase to actually cancel. It would show up as $0.00.

And if its not showing up in your Apple ID's subscriptions, then it has not activated a subscription, so nothing to cancel.