Display child posts from a certain category

You can use the post_parent argument for the query. Here is a slightly modified version of your code:

<ul class="podcasts">
    <?php 
    global $post;
    $catquery = new WP_Query( 'cat=7&posts_per_page=30&order=DESC&post_parent=" . $post->ID );
    while($catquery->have_posts()) : $catquery->the_post();?>
        <li class="track-list-item"><?php the_content();?></li>
    <?php 
    endwhile; wp_reset_postdata(); 
    ?>
</ul>

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