$category_id = get_query_var( 'cat' ); // Get current catgory ID
$category = get_term( $category_id, 'category' ); // Fetch category term object

// Now, we check if the category has a parent
// If it has, we use that ID
// If it doesn't have a parent, it is a parent category itself and we use its own ID
$parent = $category->parent ? $category->parent : $category_id;

$args = array(
    'show_count' => false,
    'hide_empty' => false,
    'title_li' => '',
    'show_option_none' => '',
    'echo' => false
);

// Show the children of parent category
if ( $category->parent ) {
    $args['child_of'] = $category->parent;
    $args['exclude'] = $category_id; // Don't display the current category in this list
}
else {
    $args['child_of'] = $category_id;
}

// Get the category list
$categories_list = wp_list_categories( $args );

if ( $categories_list ) {
    ?>
    <div class="category-wrapper">
        <ul class="child-categories">
            <?php echo $categories_list; ?>
        </ul>
    </div>
    <?php
}