As of writing, there is no direct support for push notifications as an MFA method in FusionAuth. If you would like such support, please open a feature request with more details about your use case.
However, you should be able to build something that sends a code via a push notification. Here's how to do that. (This requires a Starter, Essentials or Enterprise plan.)
This illustrates how to do this using the hosted login pages; if you use the APIs, it's a slightly different workflow, as outlined in the MFA guide.
configure FusionAuth to require a phone number when the user registers set up your android or ios device to send back the device id when the app is installed tie the device id to the user's phone number in your backend system set up a generic messenger. The messenger will send a phone number and a message when an MFA challenge occurs. look up the device id from the phone number in your system use the appropriate service to send a push notification with the code have the user enter the code in the MFA challenge screen