How to display product categories

Sry i didnt mentioned my “choose by brand (Бара?те по брендови)” is a Parent product category to all the brands they are also product categories.

I’m not sure I understand your use case enough to say whether my plugin will be suitable.

My plugin provides a widget with the letters of the alphabet as links (<a> tags). This could be placed into your header if your theme provides a widget area/sidebar in the header area. The links in the widget point to the letter in a specified page in your site provided that the page includes the shortcode.

I’m not sure about the “not redirecting them to another page” requirement. The widget points to a page that you specify in its configuration, which will require a page load when the visitor clicks on it unless the visitor is already on the specified page. However, the letters are also outputted as links to the current page as part of the shortcode output; so you don’t need the widget on the listing page itself. When the user clicks on the letters in the listing page they will be moved to the appropriate letter’s list without reloading the page.

I hope this helps, and I’m sorry if I have not understood correctly.

Sry i might forgot to mention i want the a-z listing to show on the header as child of “choose by brand” and to open in mega menu so i want when they hover over A to show brands that start with A without having to click on the letter and redirect them to another page

While my plugin can be used to create such a feature it will require custom development to implement it.

Getting the plugin to output into the header will likely need you to edit the header.php file in your theme to add either a do_shortcode() call or an the_a_z_listing() call.
You will need to write the supporting javascript for the reveal when your visitors hover their mouse over the letters. You might also need to copy the template from the plugin into your theme and edit it accordingly to support the concept.