How to add a custom vertical tab to node edit form? How can I add a block with some HTML to the Node Add/Edit form? I've tried adding a new #markup field but I couldn't position it where I need by using weight.

See image below for desired location: just below the vertical tabs displayed to the right in the Seven theme.
If you're looking insert renderable elements into the form array in the same manner as the grouped vertical tabs, you can hook_form_alter() your way to this via adding a details form element:

function MYMODULE_form_alter(&amp;$form, $form_state, $form_id) {

  // @TODO: Add your own logic for filtering relevant node forms
  if (in_array($form_id, array('node_page_form', 'node_page_edit_form'))) {
    $form['example'] = array(
      '#type' =&gt; 'details',
      '#title' =&gt; t(''),
      '#description' =&gt; t(''),
      '#group' =&gt; 'advanced',
      '#open' =&gt; TRUE,
      'markup' =&gt; array(
        '#markup' =&gt; '&lt;p&gt;Random Markup&lt;/p&gt;',
      ),
      '#weight' =&gt; 1000,
    );
  }
}


If you're looking to add markup that's not relevant to your node forms, you might be better off subtheming Seven and adding your own node-edit-form.html.twig template to your subtheme with your own markup additions:

&lt;div class="layout-node-form clearfix"&gt;
  &lt;div class="layout-region layout-region-node-main"&gt;
    {{ form|without('advanced', 'actions') }}
  &lt;/div&gt;
  &lt;div class="layout-region layout-region-node-secondary"&gt;
    {{ form.advanced }}
    &lt;p&gt;Random Markup&lt;/p&gt;
  &lt;/div&gt;
  &lt;div class="layout-region layout-region-node-footer"&gt;
    {{ form.actions }}
  &lt;/div&gt;
&lt;/div&gt;