JSFiddle - React, Tailwind, and code Playground

CSS

html, body {
    width: 100%;
    height: 100%;
}
.element {
    position: absolute;
    top: 100px;
    left: 100px;
    width: 20px;
    height: 20px;
    background : #ff0;
}

JavaScript

var $element = $("<div class='element' />");

$("body").on({
    'touchstart mousedown': function (e) {
        $element.appendTo("body");
        $(this).on('touchmove mousemove', move);
        move(e);//you could do `$(this).trigger('touchmove', e)` but a conventional function call keeps `move` simple.
    },
    'touchend mouseup': function (e) {
        $(this).off('touchmove mousemove');
    }
});

function move(e) {
    $element.css({
        left: (e.pageX - 10) + 'px',
        top: (e.pageY - 10) + 'px',
        cursor: 'pointer'
    });
}