<div class="input-group bootstrap-timepicker timepicker"><input id="timepicker" class="form-control" data-provide="timepicker" data-template="modal" data-minute-step="1" data-modal-backdrop="true" type="text"/></div>
// $('#timepicker').timepicker().on('changeTime.timepicker', function(e) {
//     var timePicked = $('#timepicker').val();

//     if(timePicked.length < 8)   
//         $('#timepicker').val("0" + timePicked);
// });

$('#timepicker').timepicker().on('changeTime.timepicker', function(e) {
    var hours=e.time.hours, //Returns an integer
        min=e.time.minutes,
        merdian=e.time.meridian;
    if(hours < 10) {
        $(e.currentTarget).val('0' + hours + ':' + min+' '+merdian);
    }
});

External CSS

  1. https://cdnjs.cloudflare.com/ajax/libs/bootstrap-timepicker/0.5.2/css/bootstrap-timepicker.css

External JavaScript

  1. https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js
  2. https://cdnjs.cloudflare.com/ajax/libs/bootstrap-timepicker/0.5.2/js/bootstrap-timepicker.min.js