The day of rendering the cheque to the bank will be considered as date of payment (if the cheque is not dishonoured latter). You are not concerned with the presentation or passing the cheque from your account.
If you deposited the cheque on 15th June and got cleared on 20th June. The date of payment will be taken as 15th June.
If the concern bank has not presented the cheque within reasonable time, the bank will be held responsible for that.
It is well settled law. You can also refer Raja Mohan Raja Bahadur v/s CIT(1967)66ITR378(SC)