How can I add special classes to only all blocks that's generated in certain region?
I am afraid this is no longer possible, according to Region-specific block templates are not available in Drupal 8.


  In Drupal 7 it was possible to specify separate block templates per
  region, such as block--header.tpl.php and block--footer.php to output
  different HTML for blocks placed in the header and footer regions. It
  was also possible to adjust variables based on region in
  hook_preprocess_block(). Both of these features have been removed.
  
  It is suggested you use standard CSS cascading selectors to style
  blocks differently on different parts of the page.


Therefore, you have 2 options:

1) In your page.html.twig you add a parent/wrapper class or id

{% if page.sidebar %}
    &lt;div class="my-sidebar"&gt;
       {{ page.sidebar}}
    &lt;/div&gt;   
{% endif %}


Then in CSS use your parent/wrapper to style your blocks .my-sidebar .block { border: solid red; }

2) Individually create a block--block--[id].html.twig for each of your sidebar blocks and add my-desired-class here.