Programmmatically adding a Custom Post

you need to specify the post_type in your $data array :

$data = array(
    'post_type' => 'classifieds',
    'post_content' => stripslashes($output),
    'post_title' => stripslashes($title),
    'post_date' => date('Y-m-d H:i:s'),
    'post_category' => array($cat_ID),
    'post_status' => $statusPost,
    'post_author' => $post_author
);