I am not registered NSR, I 'll be have a chance to blacklist

Hi
I have a health issue. I am attending a meeting. Currently, I am not been able to serve notice period with my concern. I attached the health certificate with my relieving letter.
But they threatened me you have to face an issue in future because that concern is a NASSCOM registered concern.
I need a guidance on this. Kindly help me to sort out.

Firstly NASSCOM does not maintain a employee black list register.
What are the conditions given in appointment order for notice period and exit etc?
What is the nature of illness which makes you leave without serving notice period?

nature of illness is severe back pain and headache on off
Notice period :3 months