How to show the a custom taxonomy term on single post metadata

You might be able to use the the_author_posts_link filter to do this:

add_filter( 'the_author_posts_link', functoin ($link) {

  global $post_id;

  // get "source" tax terms
  $sources = get_the_terms( $post_id, 'source' );

  // build html
  $html="";

  foreach ($sources as $source) {
    $html += '<a href="'. get_term_link($source) .'">'. $source->name .'</a>';
  }

  // pre-pend html to author link

  $link = $link . $html;

  return $link;
});

More info: https://developer.wordpress.org/reference/functions/the_author_posts_link/