My hr is giving me last working day on the last day of total notice period

Following is the seperation policy from company A)" During the period of probation your services can be terminated by either party by giving 60 days notice period or salary in lieu thereof" B) "Subject to the provision contained in the clause above, on confirmation your services shall be terminable by either party by 90 days notice period or salary in lieu thereof. Company reserves the right not to consider salary in lieu of notice period" These are exact two points in the appointment letter. I am currently in probation and my situation is as under: I have given resignation in probation period saying that i cannot serve the notice period because of personal problems and my last date will be 20 days after my resgination and I am willing to pay for the remaining notice period salary. To this the company is saying that I have to serve the complete notice period and I cannot get relieved early. When i resisted this they told me that if you dont want to work after 20 days then dont work, pay for the remaining period but your relieving letter will be issued after 60 days(meaning my last working day would be after 60 days). And experience letter will also be issued after 60 days. My questions are quite simple- 1) can they force me to work in the notice period when I am willing to pay salary for notice period? 2 ) how can they issue me a relieving letter after the complete notice period when on paper they have taken the notice period salary for the same time. Is it a legal thing or they are just trying to play smart ? What can be your suggestions in such a case?