UPDATE:
You can use onclick= function();
in the HTML.
For example:
<a-box onclick="myFunction()"></a-box>
I want to get click event of cursor with javascript from an A-frame element, like a box for example, how can I do it?
If you are using the cursor component:
box.addEventListener('click', function (evt) { // ... });
If you want to use the mouse cursor, try https://www.npmjs.com/package/aframe-mouse-cursor-component