As per Bootstrap docs:

Clicking on the modal “backdrop” will automatically close the modal.

When backdrop is set to static, the modal will not close when clicking outside it.

Via JS:

$('#myModal').modal({
    backdrop: 'static',
    keyboard: false
})

$('#myModal').modal({backdrop: 'static', keyboard: false}, 'show');

Via HTML:

<a data-controls-modal="your_div_id" data-backdrop="static" data-keyboard="false" href="#">

I found a workaround for this issue.

Once the modal has been hidden bootstrap data still remains on it. To prevent that I had the following:

$('#myModal').modal('show'); //display something
//...

// if you don't want to lose the reference to previous backdrop
$('#myModal').modal('hide'); 
$('#myModal').data('bs.modal',null); // this clears the BS modal data
//...

// now works as you would expect
$('#myModal').modal({backdrop:'static', keyboard:false});

you can try passing in the backdrop option into the modal method

j$('#apvideo').modal({backdrop:'static'});

check the bootstrap modal reference for all the available options

Ok I solved this. Maybe it is not the best solution, but it is working for my special case.

I added $('#myModal').off('click'); just after I show loading spinner on submit. This prevents from closing modal with mouse click.

There was a problem with disabling escape button, because browsers stops page loading when user press this button. So I decided to hide the spinner to unlock the form with this code:

$(document).on('keydown',function(e) {
  if (e.keyCode == 27) {
    $('#myLoadingSpinner').hide();
  }
});

Edit: I found another solution for backdrop:

$('#myModal').data('bs.modal').options.backdrop = 'static';

I tried this also for keyboard = false, but it doesn't work.