example-D7-menu-access-callbck.php

<?php

/**
 * Implements hook_menu().
 */
function MODULENAME_menu() {
  $items = [];
  $items['api/v1/sample/request'] = [
    'page callback'   => 'sample_request',
    'access callback' => 'user_is_api_user',
    'type'            => MENU_CALLBACK,
  ];
  return $items;
}

function user_is_api_user() {
  global $user;
  return (bool) ($user->name == 'api');
}

The result for users with name different of api