Leaving a job within 1 month without serving notice - Are there any legal implications or any legal action they can take?

Hi Folks, Need advice. So I joined a company where they interviewed me for something and ended up with a different job description. So it's been a month at the job and I would like to quit for a relevant job in hand. My offer letter says during probation if I wish to leave I have to serve 30 days notice but no mention of payment in lieu.

I have informed the management about my resignation before I got the salary, but they have yet to accept my resignation while asking me to stay 40 days. I'm not expecting to show this experience in my resume, so should I leave without serving the said notice period and proceed with job in hand? Are there any legal implications or any legal action they can take though I'm ready to pay the notice period?

If they have not paid you, then there is no need to serve the notice period. It is better to settle the matter amicably. Jumping the notice period is quite possible but as some of the posts in this forum show, it can have later a deleterious result later.