get current taxonomy post with ajax

//$bkcat = $term->term_id; try to call this via post from ajax where you will pass id of category
 $args = array(
'posts_per_page'   => -1,
'category'         => $bkcat,
'order'            => 'ASC',
'post_type'        => 'bk-post',
'category_name'    => $bkcat,

);
 $the_query = new WP_Query($args);
 if($the_query->have_posts()) {
        ?>

                 $i = 1;
                 while($the_query->have_posts()) : $the_query->the_post();
                 $a = $i++;

                  endwhile;
                 }

In case if you have query still let me know I will explain you entire code.