Sometimes it happens that notifications do not work in cloned apps, especially when the cloned app is in the background. Some Android devices use aggressive memory management methods, freeing up as much RAM as possible by killing apps when in the background. Depending on the device, this may also affect persistent background services used for delivering new message notifications.
What you should try here is to exclude the clone from any battery optimizations in the Android system settings as this may keep the app’s background services alive.
Using the Launching option Request ignore battery optimizations you can create clones that will automatically prompt to be added to the ignore list.
You can also try to use the option Persistent app to keep the app alive even when in the background. You should remember that persisting apps may reduce the available RAM memory, especially when creating many clones, which might have a negative impact on other apps or system performance in general.
However, sometimes notifications simply don’t work in clones, as in the case with Skype. This may be because of the internal method used to deliver notifications from the server-side components to the app, which may break for modified app certificates or package names (which is often used as an app’s unique identifier).