Hi Arshad,
Date Picker is using the jQuery library. The date format is determined by CultureCode. Could you please send us a full stack trace of the error? Are you using Calendar control with that picker? If so, custom datetime format in our calendar control is not supported scenario. The modification should be feasible in CalendarControl.ascx.cs form control. Here you should modify timePicker.DateTimeTextBox.Text to return desired format. If you decide to do this, the best practice is to make a copy of our control and do all modifications there to prevent future problems with upgrades or hotfixes.
Best regards,
Juraj Ondrus