Notice period without offer letter

Hello everyone,

I need your suggestions.

I resigned from my current company on July 16th, and as per company policy, I have a mandatory 3-month notice period. While giving interviews, I received an offer letter from Neosoft. Initially, I informed the Neosoft HR that a buyout option was available, but later my current company’s HR clarified that there is no buyout option and I must serve the full 90 days.

Neosoft has mentioned my Date of Joining (DOJ) as September 15th, but according to my notice period, my last working day in the current company will be October 15th.

Thanks