Overlap in Experience letter and PF portal

I worked for a organization for about 2.4 years. And I got selected in another organisation but new Organisation wanted me to join early in 15 days. So I had words with old organization as send them a email that out of 90 days notice period I will be able to serve 19 days notice period and for short 71 days I pay the company whatever amount they will say. I have served 19 days notice period and after that I have surrendered all the company assets. On 12th December 2021 I have resigned and served notice period of 19 days. Till 30th November and submitted all my company assets. From 1st December 2021 I stopped going to office and on 1st December 2021 I have joined a new Organisation. Later my old organization from 4th December started sending me show cause notice.I had words with HR and told that I have already informed them that I will not be able to continue after 30th November 2021 and if pay for remaining days notice period. For which they didn't agree after long mail trail they said that ok for 71 days you have to pay**** . I have paid that amount. Have all receipts and Email confirmation. But they have sent me experience letter which says that I have worked till 31st December 2021. Also they have credited December month salary in my account. And on 1st December 2021 I have joined a new Organisation now there is a 1 month overlap between my current organization and last organisation. Also the same is visible on PF portal. Now no organization is hiring me saying that you have dual employment in December 2021.