Does using event.preventDefault() in "mousedown" prevent "click" or "mouseup" event in jquery?
Neither of mouseup or mousedown prevent the default click event.
You need to use click():
$('#test').on('click', function(e) { e.preventDefault();});<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.5.1/jquery.min.js"></script><div onclick="alert('Clicked')" id="test">Click Here</div>
It does not prevent the event itself, but the action that is triggered by the event.
A simple example would be clicking on an anchor link. The default action of the click event is to take the browser to a new URL. In this case, it won't happen.