Does the terms and conditions specify one year minimum and one month notice for exit?
Reproduce the relevant terms of your appointment letter(not oppointment letter as you have written) for perusal of HR experts of the forum.
The demand on the face of it appears illegal.
Did you give resignation on email or in separate written form?
Decline to pay 3 months notice pay as claimed by them and give a proper letter drafted by a competent advocate asking for proper release and F and F.
Idea is to get a clean release and get demands from company dropped.Lawyer can advice you better.
Advice is to get a letter drafted by an advocate and not to send a legal notice.
When a lawyer drafts the letter he will cover all legal angles and be the basis of subsequent legal actions(hopefully it should be sorted out)
Legal proceedings are always last resort as law is too slow to assist ordinary petitioners and by the time relief is granted it will have no practical utility as such.
Fundamentally the company has a bond policy disguised as one year minimum period, which will not be accepted by Courts.