Modify previous and next post links to current Authors Other posts

The correct method of doing this since WordPress 4.4 is simply the following:

add_filter( "get_next_post_where", function($where, $in_same_term, $excluded_terms, $taxonomy, $post){
  $where .= " AND p.post_author="".$post->post_author.""";
  return $where;
}, 10, 5);

add_filter( "get_previous_post_where", function($where, $in_same_term, $excluded_terms, $taxonomy, $post){
  $where .= " AND p.post_author="".$post->post_author.""";
  return $where;
}, 10, 5);

Note: Please do not follow levidia1221’s accepted response, as it involves modifying WordPress Core, which is a terrible idea. Modifying the core means you can’t update WordPress without losing your changes, which is an enormous security risk. If there are no hooks present in a function you want to modify, it’s better to copy the functions you need and change them in your theme or plugin, rather than modifying the core files directly.