How to relieve in 15 days where the notice period is 2 month

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I have a question for which I need suggestions.

I have been working in an Indian IT company for the past 4 years with my overall experience of 6+ years. For the past 2 years I have been deputed onsite(abroad) and have been working at a client location. I have recently got an opportunity with a local employer here. The pay is quite lucrative and I have already made up my mind to join. My present Visa restricts me to work for any other employer unless it is transferred to the new employer.
The new employer is ready to take over the sponsorship for the existing visa but once the change of nomination is lodged with the immigration I need to join the new employer within 15 days as it is a legal requirement from immigration.
Now here's the issue....

Since I am a permanent employee of the Indian IT company and been onsite, I need to serve a minimum notice period of 2 months. Though I am not on a very critical project assignment so the current client where I am deputed should be able to relieve me without any problem and 15 days notice is good enough.
But my Indian IT company will definitely not be happy about it.

Would like to understand the best way going forward-

1) I wish to resign and give a notice of only 15 days but at the same time would try to convince the company of the visa situation.
2) I can assure them I will be available over email, phone etc during the next 2 months to ensure the new replacement can come up to speed and would support in hand over as much as possible. The company only once satisfied can provide the relieving letter post 2 months.
3) My new employer since a foreign company does not require any relieving letter but I would like to leave my present employer in a professional manner.
4) At the same time, 2 months notice is a bit too much and I can at max buy a notice period of extra 15 days (30 days in total with 15 already in my notice period).
5) How can I avoid this extra 1 month, since as per the employment contract I need to provide 2 months notice.


Is there any way where I can get the relieving letter? and what is the best approach going forward?
or should I just leave after 15 days without caring for the relieving letter at all, since as I understand most of the international labour laws enforce a notice period duration of only 15 days and most of the internation companies dont require relieving letter.

Please advice... Do let me know if further information is required.