Issue regarding relieving from duties, experience letter, and salary

I was working in one of the private university as Assistant Professor. I resigned on 15th Sept, 2018 via email as well as by submitting the hard copy of my letter with one month notice period. However, I didn't get any positive response whether my letter was accepted or not. Everything went verbally between HR and director. The appointment letter mentions only one month notice period and does not mentions about any do's and don't regarding leave during the notice period. Few faculties (especially female) who have not served even a single day after submitting resignation were given leave without pay during notice period for more than weeks duration, and also issued experience letter along with relieving letter. As per institute policy a candidate has to serve atleast 6 months for getting experience letter and I have been teaching for 8 months. I have also discussed the matter of my resignation with my director stating very clearly the unhealthy environment in institute and also my bad health condition which were major facts acting as obstacle to take proper classes. However, he told that its HR department that decides every thing and he has got no power. When contacted to HR they said it was Director who will finalize and the rolling of ball from one court to another kept on. I was on leave (absent) due to medical reason for next 10 days after which I was told that my letter is still pending for approval. However, they have conducted new interviews for faculty position to replace me but are not ready to relieve me and give experience certificate. What shall I do in this case? I have requested vice chancellor to look into the matter and have informed him that on medical cause I cannot further continue my service. Its already more than a month after submitting my letter. Regards Dr. B. Soni