As you want to put new Category attribute under Custom Design
tab then you need use tag
'group'.That means when you create attribute then you need to set group Custom Design
See Example:
<?php
$installer = $this;
$installer->startSetup();
$installer->addAttribute("catalog_category", "is_custom_field", array(
"type" => "varchar",
"backend" => "",
"frontend" => "",
"label" => "Amit Custom ",
"input" => "text",
"class" => "",
"source" => "",
"global" => Mage_Catalog_Model_Resource_Eav_Attribute::SCOPE_STORE,
"visible" => true,
"required" => false,
"user_defined" => false,
"default" => "",
"searchable" => false,
"filterable" => false,
"comparable" => false,
"visible_on_front" => false,
"unique" => false,
"note" => ""
'group' => "Custom Design"
));
$installer->endSetup();
Study Guide: here