Filter WordPress posts by custom taxonomy term with AJAX

ajax-pagination-1.php

<?php
function vb_ajax_pager( $query = null, $paged = 1 ) {

    if (!$query)
        return;

    $paginate = paginate_links([
        'base'      => '%_%',
        'type'      => 'array',
        'total'     => $query->max_num_pages,
        'format'    => '#page=%#%',
        'current'   => max( 1, $paged ),
        'prev_text' => 'Prev',
        'next_text' => 'Next'
    ]);

    if ($query->max_num_pages > 1) : ?>
        <ul class="pagination">
            <?php foreach ( $paginate as $page ) :?>
                <li><?php echo $page; ?></li>
            <?php endforeach; ?>
        </ul>
    <?php endif;
}