Date of automatic transfer of funds back to bank account?

Is there a fixed day/date when zerodha transfers the unutilized cash back to our bank account ?
what is it for quaterly and monthly settlement cycles ?

Quarterly settlement happens on the first Friday of each quarter. Monthly settlement happens only if there are no trades for a period of 30 calendar months. You can learn more about quarterly/running account settlement here:

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Thank you very much

If i have traded in last 30 days before the next Quaterly settlement then also will the unused funds on that particular friday be transferred to my bank account?

Yes, the quarterly settlement will still happen on the first Friday of each quarter.