You have already communicated your decision to resign the job and also offered to give one month notice.
Since you have not been issued with offer letter or you are aware of the terms and conditions of your employment, even this notice period is not necessary.
However, since your employer has asked you to serve three months notice period, you may write back stating that you were never given employment offer letter nor the salary slip nor you are made aware of the employment terms and conditions by which you are bound, hence the present condition imposed by the employer is not acceptable to you and you may also demand your relieving letter on the date of scheduled departure from the company and also your F&F to be settled on the the last date of working.
If the company is not acceding to your request you may issue a legal notice demanding the reliefs after which you can initiate legal action through labor law.
Consult a labor law practicing lawyer in the local and take his advise on all such further issues.