When does a notice period begin?

Hello sir/madam,

I have been working for a company since 15 November last year and I put in my resignation letter on the 30 of Nov this year. I stated in my resignation letter that I am resigning effective 29th December 2022.

After more than a week, the company says that their understanding is that I will start my notice period effective 29th December. I have sent a clarification email and an amended resignation letter stating that my notice period begins on the 30th of November and my last day of work will be the 29th of December.

The company refuses to accept this and is still sticking on to its logic and understanding and is playing on the wording of the original resignation letter.

I have another job offer and I am supposed to join them by the first week of January 2023.

Kindly advise me as to where I stand as to my legal rights!

Thanks & kind regards,