When using Firebase SDK with cloud function to send push notification, below are some of the errors I encountered and its description related to iOS.

messaging/third-party-auth-error

This error means that the authentication with the APNS failed. This is most likely due to not uploading the APNS key in the Firebase Cloud Messaging Settings.

messaging/invalid-argument

This error is thrown when there is an issue with the token. This can arise from an invalid or expired token. This could also arise when a token obtained from iOS simulator is used. It's better to test push notification using an iOS device. Later versions of Xcode supports push notification on simulator but needs additional configuration.