Notice period even when agreement has expired

Hello, I hope everyone is safe and sound in this pandemic time!! Here I am seeking help or advice. We live in Pune in a rented apartment and our agreement has expired 3 months back. We want to leave the apartment and shift somewhere else as the rent we are paying was to high compared to market price(Drastic drop in rent mainly due to COVID). We were not able to shift earlier as we were in our hometown for safety reasons in COVID times. Still, We paid rent for this 3 months. Even though the agreement has expired we were ready to give him 1 month notice so that he can search for other tenant for his apartment. We gave notice from 21st Sept to 21st October I.e. exactly 1 month. He insists that we cannot give notice in between of month and he will consider notice only from 1st of October to 1st of November. He is insisting to pay rent and will not give deposit amount till 1st of November. He tried to intimidate us by warning us that he will give us legal notice and then we will have to suffer. I find this unfair as we tried to cooperate with him and gave him notice which we are not bound to. 1. Is notice period to always start from start of month?? 2. Are we suppose to give notice period even when agreement has expired?? 3. Can owner deny our deposit considering notice period even when agreement has expired?? Will be really obliged to get your views / advice on this. Thank you in Advance!!