How to get the client id which is trying to bind my service in Android

Official android onBind method don't support you to know the caller because your service is intended to behave similarly for all clients. There are some workarounds you can try which may/may not work as the Android progress like below one.

 String callingApp = context.getPackageManager().getNameForUid(Binder.getCallingUid());

If you want to provide service based on client then its good option to create two different services for the two clients if the clients are too many then this is not a good solution. Also you can protect your service by adding signature permission so that your service will be called by only the intended client.