Trending @Infosys; Need suggestion about notice period

I am having a job offer from ABC company. My concern is the 90 days notice period of my current company which I have not told about to the HR of ABC company yet. I have only told them that I can shorten my notice period to 60 days. So, should my question is if I put up the resignation now in my current company and what if the ABC company backs off after 60 days and decides to proceed with other candidate with a notice perod possibly 30 days or lesser or is an immediate joiner.

P.S., I just got enrolled into this new project in my current company so there is no question about having responsibilities in my current project with my role here.

What should I do in such case? Please guide me and provide me suggestions.