Echo string in admin panel footer beside version no

If you look at the source:

40          <p id="footer-upgrade" class="alignright">
41                  <?php
42                  /**
43                   * Filter the version/update text displayed in the admin footer.
44                   *
45                   * WordPress prints the current version and update information,
46                   * using core_update_footer() at priority 10.
47                   *
48                   * @since 2.3.0
49                   *
50                   * @see core_update_footer()
51                   *
52                   * @param string $content The content that will be printed.
53                   */
54                  echo apply_filters( 'update_footer', '' );
55                  ?>
56          </p>
57          <div class="clear"></div>
58  </div>

You should see the filter you need, update_footer.

Something like this should do what you want:

function test_update_footer_wpse_206382() {
  return '|| Hello World';
}
add_filter( 'update_footer', 'test_update_footer_wpse_206382' );

Just before that code in the Core, there is also admin_footer_text that you might be interested in.