If your install data script successfully installed your custom attribute, now you just need to override addition information **`.phtml`** file and set your custom attribute in that.

Create **`Vendor/TestModule/view/frontend/layout/customer_account_create.xml`**

    <?xml version="1.0"?>
    <page xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" layout="1column" xsi:noNamespaceSchemaLocation="urn:magento:framework:View/Layout/etc/page_configuration.xsd">
    <body>
        <referenceContainer name="form.additional.info">
            <block class="Magento\Framework\View\Element\Template" name="additional_zipcode" template="Kage_RegisterForm::form\register.phtml"/>
        </referenceContainer>
    </body>
    </page>

Create **`Vendor/TestModule/view/frontend/templates/form/register.phtml`**

    <fieldset class="fieldset create account" data-hasrequired="<?php /* @escapeNotVerified */ echo __('* Required Fields') ?>">
        <legend class="legend"><span><?php /* @escapeNotVerified */ echo __('Additional Information') ?></span></legend>
        <p>
        <div class="field regulation">
            <label for="regulation" class="label"><span><?php /* @escapeNotVerified */
                    echo __('Additional Zipcode') ?></span></label>
            <div class="control">
                <input type="text" name="additional_zipcode" id="additional_zipcode" title="<?php /* @escapeNotVerified */ echo __('Additional Zipcode') ?>" class="input-text" data-validate="{required:false}">
            </div>
        </div>
        </p>
    </fieldset>


**`THANKS.`**