query if page has not child

$args = array(
    'post_status' => 'publish',
    'post_parent' => $post_id
);
$children = get_posts( $args );

if( count( $children ) > 0 ) {
    //has children
} else {
    //does not have children
}

Docs: get_posts()

This should also allow you to have access to the data of the children, should you need it. If you need any additional parameters in $args (a post type, for example), make sure to include those.