You are legally and contractually protected in this situation. If your offer letter clearly mentions a 1-month notice period, the company cannot force you to serve 2 months unless:
1. You later signed an amended employment agreement increasing the notice period, or
2. You formally accepted HR policies that override the offer letter.
If none of this happened, then your notice period remains 1 month, and you can lawfully leave by serving only that period. You should send an email to HR attaching the relevant clause of your offer letter and clearly stating that you will complete a 1-month notice period “as per the contract.”
Regarding late-night and weekend work during notice:
You cannot be forced to work beyond normal hours without your consent.
You may politely refuse excessive overtime, especially when it affects health or safety.
Since you have written proof of such demands, you are protected.
On background verification (BVG):
Companies are only permitted to share factual information such as employment dates, designation and whether there was any proven misconduct.
They cannot legally give negative or defamatory remarks.
Any false or damaging feedback can be challenged, and the company would be liable.
What you should do now:
1. Email HR with a copy of your offer letter and confirm your last working day after 1 month.
2. State that you will serve the contractual notice period fully and professionally.
3. Decline unreasonable overtime politely but firmly.
4. Ask HR in writing to confirm issuance of your relieving letter and experience certificate.
5. Maintain polite written communication to protect yourself if any dispute arises.