Service rule for not serving Notice period and its recovery

Hi all, My wife was serving as a assistant professor at on of Technical University in Uttar Pradesh.The University comes under UP Goverment. She had masters degree from IIT Delhi, and she served 4 years in this university since dec 2014 to dec 2018. My wife always wants to pursue PhD from US but management at university was not allowing anybody to leave from duty. Anyhow my wife applied for several US university without NOC for Phd positions and she got acceptance from one of top university in US with full funding. She didn't immediately resign but waited for visa approval. Once visa was approved she asked for study leave which was not accepted and so she resigned by mentioning last working day, 26 dec 2018, since she have to have joined school by Jan first week for spring semester. University has accepted her resignation cited that "you resignation has accepted because you haven't applied from proper channel (means not taken NOC before application), hence asked her to pay 3 months salary and get reliving. I want to mention that she served 28 days as a notice period and she asked to reduce 28 days amount with 3 months pay, they refused by mentioning clause in her offer latter that there is no provision for proportionate deduction of pay in this clause of appointment letter. Its simply mentioned . Also when she asked management to settle her 60 days Earned leave with this amount they refused to do that by saying she is not entitled to en-cash her EL at this stage. Also when she received letter for total amount to pay they asked her to pay as below: Basic Pay + Dearence Allowance + TA= 24320 + 35994 + 300 = 60,614 x3=181842 Some how they removed HRA from pay and asked her to pay remaining amount. We have there major questions as below : 1) Does she has to pay for 3 month or 3month - 28 days 2) Does she has to pay Dearence Allowance and TA since they removed HRA. 3) Does she is entitled to Encash or adjust EL in amount as above. Currently we are living in USA and my wife is doing her PhD. They send her a letter at her home and copy with email asking to submit above amount by 30 April . Otherwise they will take Administrative action. I want to mention that they hold her last month salary also she is due to receive 7th Pay Arrears. My last question is what worse they can do to her. She have a future plans to apply for potions in IITs. Please guide us. Thanks in Advance. Faizan Whatsapp no [deleted]