Company released me immediately after resigning and not paying for notice period days

Hi Concern, I am seeking advice in the matter of Labour & Employment. I work for a private firm which has a policy of putting 1 month notice period if any employee resigns, or if the company decides to terminate the employee, company will have to give 1 month notice to employee. Failing to which, either party will have to pay 1 month salary. In my case, I recently joined this company 2 months back, but I felt that this is not the kind of work I would like to do, so started looking for change. I got a verbal offer and decided to give 1 month notice to my current employer, simultaneously the company from where I had got a verbal offer gave me a joining date of 1 month later, thinking that my notice period will be served in this 1 month. Now when I resigned, I clearly stated in the email that I would like to serve 1 month notice period as per company policy. But the current company accepted my resignation from immediate effect and told me that due to business shortage, the very same day would be your last day. To be exact, I put a notice on 13th Aug, I had a joining date from another company for 13th Sept. But company released me on 13th Aug only. Now, I have nothing left for 1 month, I will be loosing the salary for 1 month and I can only start in the new company from 13th Sept. When I talked to my employer that since you released me from immediate effect and I was ready to serve the notice period also, you should pay me for 1 month. But they are completely denying that. They are telling that we would have paid you 1 month salary if we would have terminated you. In your case, you resigned, and we accepted the same day and released you the same day, so we are not obliged to pay any further amount to you. I want to get more clarification on this.