It is not possible to edit the uID registration form, the registration form and the fields in it are the same for all websites that support uID.

It is possible to change/edit the local registration form.

To change the fields of the registration form go to Control Panel -> Users -> Module settings -> Fields of the registration form:
There are two columns of checkboxes near each field name. The first checkbox enables/disables a field, the second checkbox makes the field required/optional.

The default field names can be changed in Control Panel -> Substitution of default phrases -> Form for registering new site users. i.e. you can change the names into any names you need.

You can edit the template code of the registration form in Control Panel -> Customize Design -> User registration form and the code of the registration page in Control Panel -> Customize Design -> User registration page.

If the default registration form is not working, it is desirable to check the following:

!) JavaScript must be enabled in your browser;

!) your browser must accept cookies;

!) there can be a script conflict if you use third-party JavaScript or jQuery versions, incompatible with the uCoz jQuery version.

Quick links:

1. The checkmark "I agree to the terms" in the registration form (local form)