My app badge count in not increasing when app is in background for push notifications.Count increase by 1 only for the first push notification and always remains badge count
You said your payload is :
aps = { alert = "third testing"; badge = 1; sound = "sound.caf"; };
Since you always send 1 for badge count, that's the badge count being displayed for your app. The badge count is not incremental. If you want to see badge counts higher than 1, your server should put values higher than 1 in your payload.
Your server should keep track of which badge count each device should receive. The app itself is not guaranteed to receive all the push notifications, so you can't rely on its logic to update the badge count.