JSFiddle - React, Tailwind, and code Playground

HTML

<p id="menu">HOVER FOR MENU</p>
<ul id="schnellsuche_box">
    <li>clicking</li>
    <li>here</li>
    <li>will not</li>
    <li>close this</li>
    <li>box</li>
</ul>

CSS

#schnellsuche_box {display: none; width: 200px; height: 200px; background: grey; position: relative;}

JavaScript

$('#menu').on('mouseenter', function() {
    $('#schnellsuche_box').show();
});

$(document).on('click', function(e) {
    if ( ! $(e.target).closest('#schnellsuche_box').length ) 
         $('#schnellsuche_box').hide();
});