Should I serve the notice period?

Hello.
My employer (X organization) says it can sue me for breaching the terms of the offer letter. But the offer letter doesn't mention anywhere that I've to serve one month of notice period if I leave during the probation period. I resigned while I was on probation and now he's talking vigorously. During the interview calls or onboarding process and all the other written/verbal communication, he did not mention that I am liable for serving the notice period of one month.

Dear Colleague,

The documents you need to check for notice period are-
- The Offer Letter
- The Appointment Order
- The employment Contract
- The Service Rules or Conditions
- HR Policy Manual of the company
- Standing Order if any and applicable for you

If all the documents are not having any clause on your notice period service condition, then you can decide suitably and if all documents does not speak about Notice Period, then in such case, no suit will be legal. Hence check before deciding.