Widget with option to select a parent page. The widget shows the parent with a list of subpages below.

subpage-list-widget.php

<?php

/*
Plugin Name: Subpage List Widget
Description: A widget to list the subpages of a page.
Version: 1
Author: GuRuStu.co
Author URI: http://gurustu.co
*/
/**
 * Adds Featured_Pages_Widget widget.
 */
class GRS_Subpage_List_Widget extends WP_Widget {

    /**
     * Register widget with WordPress.
     */
    public function __construct() {
        parent::__construct(
            'grs_subpage_list_widget', // Base ID
            'Subpage List Widget', // Name
            array( 'description' => __( 'A widget to list the subpages of a page. ', 'text_domain' ), ) // Args
        );
        
    }

    /**
     * Front-end display of widget.
     *
     * @see WP_Widget::widget()
     *
     * @param array $args     Widget arguments.
     * @param array $instance Saved values from database.
     */
    public function widget( $args, $instance ) {

        extract( $args );
        echo $before_widget;

        // This is the output for the widget on the frontend

        ?>
        <div class="col-md-4">
            <h1 class="footer-heading">
                <a class="footer-heading" href="<?php echo get_permalink($instance['page_id']); ?>"><?php echo get_the_title($instance['page_id']); ?></a>
            </h1>
            <ul>
                <?php wp_list_pages("title_li=&child_of=" . $instance['page_id']); ?>
            </ul>
            <br>
        </div>
        
        <?php
        
        echo $after_widget;
    }

    /**
     * Sanitize widget form values as they are saved.
     *
     * @see WP_Widget::update()
     *
     * @param array $new_instance Values just sent to be saved.
     * @param array $old_instance Previously saved values from database.
     *
     * @return array Updated safe values to be saved.
     */
    public function update( $new_instance, $old_instance ) {
        $instance = array();
        $instance['page_id']      = $new_instance['page_id'];
        return $instance;
    }

    /**
     * Back-end widget form.
     *
     * @see WP_Widget::form()
     *
     * @param array $instance Previously saved values from database.
     */    
    public function form ( $instance ) { ?>
        <p>
        <label>Select a parent page:</label>
        <select name="<?php echo $this->get_field_name('page_id'); ?>" id="<?php echo $this->get_field_id('page_id'); ?>">
        
            <?php 
                $id = $instance['page_id'];
                $pages = get_posts(array('post_type'=>'page', 'posts_per_page'=> -1));
                foreach( $pages as $page ){
                    $children = get_posts(array('post_type'=>'page', 'post_parent' => $page->ID));
                    if( count($children) > 0 ){

                        if( $page->ID == $id ){
                            $selected = 'selected';
                        } else {
                            $selected = '';
                        }
                        echo '<option value="'.$page->ID.'" ' . $selected . '>'.$page->post_title.'</option>';

                    }
                }

            ?>

        </select>
        </p>
        <?php
    }

} // class 
add_action( 'widgets_init', function(){
    register_widget('grs_subpage_list_widget');
});

?>