How can get access to field's data of plugin block in twig template?
you can use markup render arrays like this:

 public function build() {
    $build = [];

    $build['LinkA_url'] = ['#markup' =&gt; $this-&gt;configuration['LinkA_url']];
    $build['LinkB_url'] = ['#markup' =&gt; $this-&gt;configuration['LinkB_url']];

    return $build;
  }


Then in your twig:

  &lt;p&gt;&lt;a href="{{ content.LinkA_url }}"&gt;link 1&lt;/a&gt;&lt;/p&gt;
  &lt;p&gt;&lt;a href="{{ content.LinkB_url }}"&gt;link 2&lt;/a&gt;&lt;/p&gt;


then add hook_theme in your .module file:

/**
 * Implements hook_theme().
 */
function my_module_theme() {
  return array(
    'block__my_module' =&gt; array(
      'base hook' =&gt; 'block'
    ),
  );
}


Otherwise, it won't look in your module's templates folder.