Early relieving - No Appointment Letter - No policies in Organization

Dear All,
I am Giridhar, 4 months back joined in an organisation where there are no policies and even they haven't given the appointment letter. They have taken me for program management role and made me to work in supply chain department also.
Now I got a new opportunity and Want to relieve early, but here they are saying 3 months notice period is must. I have explained my situation that the new employer is not extending my date of joining and I am in the verge of becoming unemployed.
So my manager accepted and he said he will relive me before the joining date but now HR is saying we cannot relieve you before 3 months. Please suggest me what can I do now to get early reliving.
Regards,
Giridhar

Hi,
Hai Giridhar, First confirm your job profile like Company appointment or Contract.

Hi Lakshmi,
I am working as a Assistant Manager in program management department in Pharma company.
I am a direct employee. here just 4.5 months back I have joined.
There is no appointment letter in this organisation, I haven't signed any where. but when I have put my resignation they are asking me to stay for 3 months. I have asked them with in 6 months I have out my resignation, and even I said I can stay 1 month , more than that I cannot. still they are not giving any confirmation on my relieving. So can you please suggest what can I do.

Can any one please suggest what to do?