<?php
$categories = get_categories('child_of=4');
foreach ($categories as $category) {
echo '<li><a href="' . get_category_link($category->cat_ID) . '" title="' . $category->name . '">' . $category->name . '</a></li>';
foreach (get_posts('cat='.$category->term_id) as $post) {
setup_postdata( $post );
}
}
?>
here 4 is your category id .
