I've three pages during my WordPress site: About, Voices &lifier History. They are all utilizing the same template. All these are parent pages to many additional particular sub-pages (i.e. About is parent to 5 About sub-pages). All the parent pages make use of the same sidebar.php file.

Is it feasible for that sidebar to show just the parent's particular sub-pages?

For instance, when the user is around the About page, the sidebar would query and just display About sub-pages. If they are around the Voices page, the sidebar changes to show only Voices sub-pages.

I have been not successful during my attempts. Any code to do this is greatly appreciated.

What you might do is, in your soul loop do that:

//calling loop stuff here
// bla bla
// stores post that will have related posts
global $related;
$related = $post->ID;
// end loop

Then, inside your sidebar you need to do this:

//common sidebar stuff here
//bla bla
//check if has related posts
global $related;
if (!empty($related)) {
//call related posts here