Load custom script on a single template

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Multiple issues, fixing one or more of which should resolve the issue:

  1. If it’s not already, that code should go in functions.php and not a template file.
  2. Registering the scripts does not actually load them. For that you need wp_enqueue_script. If you change your wp_register_scripts to wp_enqueue_scripts, that should work.
  3. If you need jquery, you should enqueue that too.
  4. You want to wrap the calls to wp_enqueue_script in the conditional rather than add_action. For instance, you might want to enqueue a different script on a different page and could do so within the same function.

Put those all together and you should have this in functions.php:

<?php
function my_enqueue_scripts() {
    if (is_page_template('page_blankett.php')){
        wp_enqueue_script('jquery');
        wp_enqueue_script('ajax', plugins_url('ajax.js', __FILE__), array('jquery'),   'false', 'true' );
        wp_enqueue_script('ajax2', plugins_url('ajax2.js', __FILE__), array('jquery'), 'false', 'true' );
    }
}
add_action( 'wp_enqueue_scripts', 'my_enqueue_scripts' );
?>