Change sub-menu position of custom taxonomy

Unluckily does not exist a clean way to do this, because register taxonomy doesn’t provide a menu_order argument.

But you can act on global $submenu variable and reorder it, something like

add_action( 'admin_menu', function() {
  global $submenu;
  $found = FALSE;
  $before = $after = array();
  $tax_slug = 'my_custom_tax'; // change your taxonomy name here
  foreach ( $submenu['edit.php'] as $item ) {
    if ( ! $found || $item[2] === 'edit-tags.php?taxonomy=' . $tax_slug ) {
      $before[] = $item;
    } else {
      $after[] = $item;
    }
    if( $item[2] === 'edit-tags.php?taxonomy=category' ) $found = TRUE;
  }
  $submenu['edit.php'] = array_values( array_merge( $before, $after ) );
}, 0 );