Use twig to style a specific block (unformated list)
Not sure to understand what you mean...

Do you want to customize the fields that appear in your block?? If so, Drupal normally provides you with available twig hooks you could use. Yours would probably be field.html.twig.

Exemple : you can customize a menu with menu.html.twig and then customize the links in that menu with links.html.twig