Show subterms in a page
Taxonomy VTN provide new pages for taxonomy terms, as described in its page it provide what you want by Terms of a parent: taxonomy_vtn/voc/xxx/xxx option

in Drupal 7 you can use views to show child terms in page when you click on parent term:


create new views for taxonomy terms (you should select taxonomy terms in creation form)
create page display
select taxonomy/term/% as path
use argument