Notice periods during probation

I am employed on a probationary basis for 12 months in an organisation. My date of joining is 11 jan and I resigned on the 2nd Feb. My company policy on the company portal says that an employee who has joined after 4 th Jan of 2021 and is still on probation is required to serve a 30 days notice. My offer letter has no clause regarding the notice period during probation but a general clause which states that the employer can terminate giving a 90 days notice by paying a pro rata salary and the employee should give a 90 days notice and the buyout if applicable will be solely at discretion of the employer. Now the issue is they neither have given me a 30 days nor a 90 days notice but a 60 days notice period. Even after I showed the policy of the organisation to the HR ,she is saying that I have to serve a 60 days notice and not allowing me to buyout the 30 days notice period. I am really confused on what grounds I am asked to serve this notice period as it doesn't adhere to the offer letter clause nor to the company policy mentioned on the company portal . What are my options?