test.js

import { RequestMock } from 'testcafe';

const mock = RequestMock()
    .onRequestTo(/http:\/\/localhost:8080\/api\/test\/.*/)
    .respond((req, res) => {
        res.headers['access-control-allow-origin'] = '*'; // It's necessary because TestCafe load the page via file protocol in this example.

        const dateUrlPart = req.path.replace('/api/test/', '');

        res.setBody({
            date: dateUrlPart, 
            data: 'my cool data'
        });
    });

fixture `Fixture`
    .page('./index.html')
    .requestHooks(mock);

test('test', async t => {
    await t.click('#sendRequestBtn').wait(1000);
});