How to make a radio button unchecked by clicking it?

You can set HTML object’s property checked to false like this:

document.getElementById('desiredInput').checked = false;

Examples

Plain JavaScript:

var radios = document.getElementsByTagName('input');
for(i=0; i<radios.length; i++ ) {
    radios[i].onclick = function(e) {
        if(e.ctrlKey || e.metaKey) {
            this.checked = false;
        }
    }
}
<input type="radio" name="test" value="1" />
<input type="radio" name="test" value="2" checked="checked" />
<input type="radio" name="test" value="3" />

jQuery:

$('input').click(function(e){
    if (e.ctrlKey || e.metaKey) {
        $(this).prop('checked', false);
    }
});
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<input type="radio" name="test" value="1" />
<input type="radio" name="test" value="2" checked="checked" />
<input type="radio" name="test" value="3" />

Hold down Ctrl ( on mac) key to uncheck.

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