How to determine the notice period in a Free zone company?

Hello,

I am working in a private company in Ras Al Khaimah, UAE with a Freezone visa. I want to know the legal point of view about the notice period. I got a better opportunity to grow in my career and I am ready to serve 30 days notice period and the balance I agreed to pay.

However, my current company is insisting to serve 60 days' notice whereas my new company will not wait for 60 days. They can wait up to 35 days maximum.

In my contract with Freezone, the notice period is blank however there is an internal memo that I have acknowledged for 60 days notice period, so I want to check the legal point of view in this matter.