Observable which does not pass anything in onNext()

You don’t need to call onNext if your Observable doesn’t emit anything.
You could use Void in your signature and do something like

Observable<Void> o = Observable.create(new Observable.OnSubscribe<Void>() {
    @Override
    public void call(Subscriber<? super Void> subscriber) {
        // Do the work and call onCompleted when you done,
        // no need to call onNext if you have nothing to emit
        subscriber.onCompleted();
    }
});

o.subscribe(new OnCompletedObserver<Void>() {
    @Override
    public void onCompleted() {
        System.out.println("onCompleted");
    }

    @Override
    public void onError(Throwable e) {
        System.out.println("onError " + e.getMessage());
    }
});

You can define an OnCompletedObserver to simplify your Observer callback so that you don’t have to override the onNext since you don’t need it.

public abstract class OnCompletedObserver<T> implements Observer<T> {
    @Override
    public void onNext(T o) {

    }
}

If I’ve understood what you’re asking then this should do the trick.