Regarding Notice period of 30 days

Respected Sir / Ma'am I was working with Delhi based Recruitment company I joined on July 19th 2021. After joining they released an appointment letter. HR asked me to sign all the pages and returned him with photo copy / Duplicate copy. But due to work load / Work pressure, I didn't sign that appointment letter and never returned the same as duplicate copy. I worked there for 5 months but since due to distance issues (2 hours journey from one side) , I requested HR to release me without serving notice period. I wrote resignation on email and requested them to waive off my notice period. But they replied that they accepts my resignation but they will follow the exit formalities as per the company policy. I requested them that I don't need 16 days salary in fnf and don't require any experience certificate as well, if they relieve me immediately. By next day, HR called me on phone and said you can relieve immediately and come office to handover your laptop and database, which I did so. And then they relieved me. I left the company on Dec 16th 2021. But they didn't give me anything in writing that they have relieved me successfully. Because it was in good faith. After a week they came to know I have joined another company which is nearest to my home (25 mins), and then today on Jan 31st, they have send me a legal notice through advocate that since I didn't serve Notice period of 30 days so I need to pay remaining amount within 15 days plus 9% interest. Here my question is I didn't sign any bond , appointment letter, wrote resignation on email and didn't take my 16 days salary. After all this, am I need to pay the said amount in legal notice. Please suggest me the way forward Thanks in advance!