Custom Style for Menu Item with Categories in Wordpress, connected with https://gist.github.com/igorveremsky/63692b1e4718849c3f93992bc7ad783e

header.php

    <?php
                class CustomStyleForMenuItemWalker extends Walker_Nav_Menu {
                    function start_el( &$output, $item, $depth = 0, $args = array(), $id = 0 ) {
                        // add classes for menu item
                        $class_names = join( ' ', $item->classes );
                        $class_names = ' class="' .esc_attr( $class_names ). '"';
                        $output.= '<li id="menu-item-' . $item->ID . '"' .$class_names. '>';

                        //first get the current category ID
                        $cat_id = $item->object_id;

                        //then i get the data from the database
                        $cat_data = get_option("category_$cat_id");

                        //and then i just display my category image if it exists
                        $cat_custom_color = $cat_data['custom_color'];

                        // add attributes for link
                        $attributes = !empty( $item->url ) ? ' href="' .esc_attr($item->url). '"' : '';
                        $item_output = $args->before;

                        // add custom style for category
                        if ($cat_custom_color) {
                            $item_output .= <<<EOT
<style>
li#menu-item-{$item->ID}:after {
background: #{$cat_custom_color};
}
#site-sidebar #site-navigation .menu > li#menu-item-{$item->ID} a:hover,
#site-sidebar #site-navigation .menu > li#menu-item-{$item->ID}.current-menu-item > a {
color: #{$cat_custom_color};
}
</style>
EOT;
                        }

                        $item_output .= '<a'. $attributes .'>'.$item->title.'</a>';

                        $item_output.= $args->after;
                        $output.= apply_filters( 'walker_nav_menu_start_el', $item_output, $item, $depth, $args );
                    }
                }

                wp_nav_menu( array(
                    'theme_location' => 'category',
                    'walker' => new CustomStyleForMenuItemWalker()
                ) ); ?>