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});

Hi @anonymouse703

Which version of Bootstrap are you using?

Try replacing
data-backdrop="static" data-keyboard="false"

with
data-bs-backdrop="static" data-bs-keyboard="false"

post Bootstrap v5, we have to use data-bs-*

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

On Options chapter, in the page you linked, you can see the backdrop option. Passing this option with value 'static' will prevent closing the modal.
As @PedroVagner pointed on comments, you also can pass {keyboard: false} to prevent closing the modal by pressing Esc.

If you opening the modal by js use:

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

If you are using data attributes, use:

 <button data-target="#myModal" data-toggle="modal" data-backdrop="static" data-keyboard="false">
    Launch demo modal
 </button>`