Hello blane147,
Thank you for reaching out in Apple Support Communities. You'll want to make sure that the controller by Nintendo can be connected to an iPhone via Bluetooth. This is a good question to contact Nintendo about and to verify that information. If it is compatible, then we suggest for you to follow these steps as it can help:
If the controller doesn't connect or work as expected
Support for specific buttons and features, such as a controller's audio jack or lights, varies by controller and the app you're using with it.
* Install the latest software updates—both for your Apple device and the controller. If a software (firmware) update is available for the controller, get it from the maker of the controller.
* In Bluetooth settings, select the controller or the info button (if present) next to its name, then select Forget This Device. Connect the controller again.
* Reduce the number of Bluetooth devices connected to your Apple device. This can also help with connection issues related to wireless interference. Apple TV 4K and Apple TV HD support up to four Bluetooth game controllers at the same time, or one controller when Apple TV is also using a Bluetooth audio accessory. The limit for other Apple devices varies based on your specific setup and wireless environment.
* To charge your controller, use the charging solution included with your controller or recommended by the controller manufacturer.
Following these steps may help and is outlined in this article: Connect a wireless game controller to your Apple device - Apple Support
Kind regards.