How to add new tab to admin list of posts and handle result list

Admin post queries can be filtered just like frontend queries using pre_get_posts and checking for is_admin.

add_action( 'views_edit-post', 'remove_edit_post_views' );
function remove_edit_post_views( $views ) {
    $views['pre'] = '<a href="'.admin_url().'edit.php?pre=pre">My Special Posts</a>';
    return $views;
}

add_action('pre_get_posts', 'my_special_list');

function my_special_list( $q ) {
  $scr = get_current_screen();
  if ( is_admin() && ( $scr->base === 'edit' ) && $q->is_main_query() ) {
    // To target only a post type uncomment following line and adjust post type name
    // if ( $scr->post_type !== 'post' ) return;
    // if you change the link in function above adjust next line accordingly
    $pre = filter_input(INPUT_GET, 'pre', FILTER_SANITIZE_STRING);
    if ( $pre === 'pre' ) {
      // adjust meta query to fit your needs
      $meta_query = array( 'key' => 'is_special', 'value' => 'yes', );
      $q->set( 'meta_query', array($meta_query) );
    }
  }
}