"So I contacted Asus customer care and told them regarding my issue on that they said there should be no damage and breakage only then they could repair it under warranty otherwise you would have to pay for the screen which is around 16000 INR."
That's the standard warranty. If the phone had a defect, ASUS will fix it under warranty. If the repair center finds accidental damage that led to the panel failure, ASUS will not fix it under warranty. If you haven't dropped it, you should have nothing to worry about.
Have you taken the phone to a service center yet? It sounds like Support has given you options for a repair, even if it is found to be accidental damage.