How to List Thumbnails based on Custom Categories

You need to use custom post and make the categorys there and align the thumbnails in each post.

 <?php // query post type */*/

        global $post;
        $args = array(
        'post_type' => 'YOUR-POST-TYPE-HERE',
        'cat' => $category,
        'suppress_filters' => '0',
        'numberposts' =>'-1',
        'orderby' => 'title',
        'order' => 'asc',
        'post_status' => 'publish' );   
        $myposts = get_posts( $args );

        foreach( $myposts as $post ) :  setup_postdata($post);
        $meta = $custom_metabox_jurister->the_meta();?>

And check if post have thumnail:

<?php // Checks if there is a thumbnail and displays it
                if ( has_post_thumbnail() ) { 

                $size="thumbnail";
                $attr = array(
                'class' => 'post-logo');
                echo '<div class="image">';
                echo the_post_thumbnail('large', $attr);
                echo '</div>';
                } 
                else{ 
                // Do nothing
                } 
    ?>

Change the code , to fit your idea.

Not sure if I understood exactly what you wanted to do. But hope this helps.