Значок на значке приложения в приложении для iPhone

Вы можете установить номер значка значка приложения следующим образом:

[UIApplication sharedApplication].applicationIconBadgeNumber = 3;

Если вы хотите поместить номер значка в PUSH-сообщения, вы можете отправить PUSH как:

{"aps":{"alert":"My Push Message","sound":"default","badge",3}}

Затем в своем AppDelegate вы добавляете следующее:

- (void)application:(UIApplication *)application didReceiveRemoteNotification:(NSDictionary *)userInfo{

// This get's the number you sent in the push and update your app badge.
[UIApplication sharedApplication].applicationIconBadgeNumber = [[userInfo objectForKey:@"badge"] integerValue];

// Shows an alert in case the app is open, otherwise it won't notify anything
UIAlertView *alertView = [[UIAlertView alloc] initWithTitle:@"New Notification!"
                                              message:[[userInfo objectForKey:@"aps"] objectForKey:@"alert"]  delegate:self
                                              cancelButtonTitle:@"OK"
                                              otherButtonTitles:nil];
[alertView show];    
}

быстро:

func application(_ application: UIApplication, didReceiveRemoteNotification userInfo: [AnyHashable : Any]) {

// This get's the number you sent in the push and update your app badge.
UIApplication.shared.applicationIconBadgeNumber = (userInfo["badge"] as? NSNumber)?.intValue ?? 0

// Shows an alert in case the app is open, otherwise it won't notify anything
let alertView = UIAlertView(title: "New Notification!", message: (userInfo["aps"] as? [AnyHashable : Any])?["alert"], delegate: self, cancelButtonTitle: "OK", otherButtonTitles: "")
alertView?.show()
}