There's no "file to edit" for this. But using the javascript extension API, you can extend the LogInModal
component, and add content to the fields
or footer
ItemLists.
Example, untested:
extend(LogInModal.prototype, 'fields', function (items) {
items.add('my-field', m('p', 'Hello World'), 100);
});
One extension that can give some examples to manipulate the login modal is my passwordless extension clarkwinkelmann/flarum-ext-passwordlessblob/master/js/src/forum/index.ts
I don't think we have any extension that just provides the ability to insert arbitrary text to the login modal, but it wouldn't be something to develop since that would just be my example code above coupled with a setting in the admin to store the content and a forum serializer extender to make it available to the frontend.