How to show terms used only for particular custom post type. Filter creation perpose

Question

You need to send param post_id in ajax of data. Then in your plugin parse it and and search by taxomony.
My simple example:

<?php 
// in ajax handler
// get post_id from requst data
$post_id = filter_var($_POST['post_id'], FILTER_VALIDATE_INT);
// find post
$post = get_post($post_id);

But before you need register the taxomony.

register_taxonomy('auto', array($post->post_type), array(
    'label'                 => '', // определяется параметром $labels->name
    'labels'                => array(
        'name'              => 'auto',
        'singular_name'     => 'auto',
        'search_items'      => 'Search auto',
        'all_items'         => 'All auto',
        'view_item '        => 'View auto',
        'parent_item'       => 'Parent auto',
        'parent_item_colon' => 'Parent auto:',
        'edit_item'         => 'Edit auto',
        'update_item'       => 'Update auto',
        'add_new_item'      => 'Add New auto',
        'new_item_name'     => 'New auto Name',
        'menu_name'         => 'Auto',
    ),
    'description'           => '', // описание таксономии
    'public'                => true,
    'publicly_queryable'    => null, // равен аргументу public
    'show_in_nav_menus'     => true, // равен аргументу public
    'show_ui'               => true, // равен аргументу public
    'show_tagcloud'         => true, // равен аргументу show_ui
    'show_in_rest'          => null, // добавить в REST API
    'rest_base'             => null, // $taxonomy
    'hierarchical'          => false,
    'update_count_callback' => '',
    'rewrite'               => true,
    'capabilities'          => array(),
    'meta_box_cb'           => null, // callback функция. Отвечает за html код метабокса (с версии 3.8): post_categories_meta_box или post_tags_meta_box. Если указать false, то метабокс будет отключен вообще
    'show_admin_column'     => false, // Позволить или нет авто-создание колонки таксономии в таблице ассоциированного типа записи. (с версии 3.5)
    '_builtin'              => false,
    'show_in_quick_edit'    => null, // по умолчанию значение show_ui
) );

and register terms

wp_set_object_terms($post_id, ['audi', 'bmw', 'kia'], 'auto');

Finaly you need send response

    ob_start();
// Build an array of taxonomies slugs to be used in our $args array below to filter only taxes we need.
foreach ($cpt_taxes as $cpt_tax) {
    $cpt_tax_name = $cpt_tax->name;
    $cpt_tax_label = $cpt_tax->labels->singular_name;
    ?>
    <li class="accordion-item " data-accordion-item>
        <!-- Accordion tab title -->
        <a href="#" class="accordion-title"><span><?php echo $cpt_tax_label; ?>
    </span></a>
        <!-- Accordion tab content -->
        <div class="accordion-content" data-tab-content>
            <?php
            $terms_list = (array)get_terms([
                                               'taxonomy'   => $cpt_tax_name,
                                               'orderby'    => 'name',
                                               'hide_empty' => true,
                                           ]);
            foreach ($terms_list as $term_data) {
                echo '<input id="' . $term_data->name . '" type="checkbox" name="' . $term_data->name . '"><label for="' . $term_data->name . '">' . $term_data->name . ' <small>(' . $term_data->count . ')</small></label> <br>'; // ID of the category as the value of an option
            } ?>
        </div>
    </li>
    <?php
}
$html = ob_get_clean();

wp_send_json_success($html);
wp_die();

My code on github https://github.com/ggmanuilov/wpajaxtaxomony/tree/master

I hope I could help you.

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