Wrong Last Working Day Mentioned In Relieving Letter

Dear team I resigned on 5th July and my notice period was 3 months, I served till 24th September and as per 3 months notice period my last working day was 2nd October.... But since I had to join other organization on 27th September I sent multiple mails for relieving me just 5 days earlier from my last working day. When I didn't get any confirmation I myself sent declaration mail for my last working day as 24th September and also wrote that I am ready to compensate against my remaining notice period as per HR policy. I joined other organization on 27th September but my previous organization intentionally mentioned last working day as 2nd October After getting relieving also I sent multiple mails for correction of date but didn't get any help Please suggest what steps can be taken against my previous employer for this unethical behavior...