This question is actually an extension of this question.

For default post type posts are populated based on category selection from the drop down, but when I change the settings for the Custom post types than posts do not populate for the CPT categories election from the drop down.

I think that the ajax part of the scripting is working fine. Check the visual here. But the conditional loop has some issue.

Here is the code →

/ Script for getting posts
function ajax_filter_get_posts( $taxonomy ) {

  // Verify nonce
  if( !isset( $_POST['afp_nonce'] ) || !wp_verify_nonce( $_POST['afp_nonce'], 'afp_nonce' ) )
    die('Permission denied');

  $taxonomy = $_POST['taxonomy'];

  if($taxonomy == 'all'){
      // WP Query
      $args = array(
        'post_type' => 'video',
        'posts_per_page' => -1,
      );
  }else{
      // WP Query
      $args = array(
        'category_name' => $taxonomy,
        'post_type' => 'video',
        'posts_per_page' => -1,
      );
  }

  // If taxonomy is not set, remove key from array and get all posts
  if( !$taxonomy ) {
    unset( $args['category'] );
  }

  $query = new WP_Query( $args );

  if ( $query->have_posts() ) : while ( $query->have_posts() ) : $query->the_post(); ?>
    <li class="box">
        <div class="images"><?php the_post_thumbnail( 'large') ?></div>
        <div class="text3">
            <h4><?php $categories = get_the_category();
            if ( ! empty( $categories ) ) {
              echo '<a class="themelor" href="' . esc_url( get_category_link( $categories[0]->term_id ) ) . '">' . esc_html( $categories[0]->name ) . '</a>';
            } ?></h4>
            <h3><a href="<?php the_permalink(); ?>" title="<?php the_title_attribute(); ?>"><?php the_title(); ?></a></h3>
        </div>
    </li>
  <?php endwhile; ?>
  <?php else: ?>
    <h2>No posts found</h2>
  <?php endif;
  //die();
    exit();
}

add_action('wp_ajax_filter_posts', 'ajax_filter_get_posts');
add_action('wp_ajax_nopriv_filter_posts', 'ajax_filter_get_posts');

I think this part is executing →

      if($taxonomy == 'all'){
      // WP Query
      $args = array(
        'post_type' => 'video',
        'posts_per_page' => -1,
      );
  }else{

But this part is not executing →

      $args = array(
    'category_name' => $taxonomy,
    'post_type' => 'video',
    'posts_per_page' => -1,

Can some one help me where am I going wrong? what need to be fixed in the loop?

#Extra: Category for CPT is defined like this:

    add_action( 'init', 'create_video_cpt_taxonomy' );

function create_video_cpt_taxonomy() {
    register_taxonomy(
        'vcategory',
        'video',
        array(
            'label' => __( 'Video Category' ),
            'rewrite' => array( 'slug' => 'vcategory' ),
            'hierarchical' => true,
        )
    );
}

add_action( 'init', 'video_CPT_registration' );

For custom post types do we have to write this part in some other way:

      $taxonomy = $_POST['taxonomy'];

Or perhaps there is something else that is conflicting.

Please let me Know if I have to give some extra information.

#Update as requested →

<?php
            wp_dropdown_categories( array(
                'show_option_all'    => 'All',
                'orderby'            => 'name',
                'order'              => 'ASC',
                'hide_empty'         => 1, // change to 0 if empty terms should be shown to
                'echo'               => 1,
                'selected'           => 0,
                'name'               => 'categoryfilter',
                'taxonomy'           => 'vcategory',
                'value_field'        => 'slug',
            ) );
        ?>