Add tabs on node edit page
You need to define a new URL by using hook_menu. 

There, 'type' is set as MENU_LOCAL_TASK and URL is like 'node/%node/CUSTOM_CONFIG'.

Code snippet from the hook_menu in node.module:

 $items['node/%node/edit'] = array(
    'title' =&gt; 'Edit',
    'page callback' =&gt; 'node_page_edit',
    'page arguments' =&gt; array(1),
    'access callback' =&gt; 'node_access',
    'access arguments' =&gt; array('update', 1),
    'weight' =&gt; 0,
    'type' =&gt; MENU_LOCAL_TASK,
    'context' =&gt; MENU_CONTEXT_PAGE | MENU_CONTEXT_INLINE,
    'file' =&gt; 'node.pages.inc',
  );