Get custom fields when hover link of post

I would just put the custom fields in the <li> after the <a> and then show/hide them with your preferred tooltip method, whether it be CSS, JS or a combination of the two:

<?php

if( $my_query->have_posts() ) {
    while ($my_query->have_posts()) : $my_query->the_post(); ?>
        <li>
            <a href="https://wordpress.stackexchange.com/questions/155135/<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title_attribute(); ?>" target="_blank"><?php echo str_replace($xx,'',get_the_title()); ?></a>
            <div>description, post-image, etc go here</div>
        </li>
    <?php
    endwhile;
}
?>