Hi,
To show the thumbnail you need to modify the template that the plugin uses. Copy the file at wp-content/plugins/a-z-listing/templates/a-z-listing.php
into your theme’s folder and modify as follows:
Add a new line beneath line 54 with:
$post = $a_z_query->get_the_item_object();
Then inside the <li>
on line 56 thru 60 add (probably on line 58 as part of the link):
<?php echo get_the_post_thumbnail( $post, 'post-thumbnail', '' ); ?>
The second item on the function call which is set to post-thumbnail
above needs to be an image size that is provided by your theme. See the get_the_post_thumbnail() documentation on www.remarpro.com for information on using the function, which is part of WordPress.