Through Google Search Console, you get insight into the effect of your search results on visitors in Google. The big difference between Google Search Console and a tool like Google Analytics is that Search Console makes your search results in Google measurable, where Analytics provides insight into the behaviour of website visitors who have already landed on your website. Google Search Console is an advanced tool for understanding what data Google uses to rate your site. It is certainly useful for your clone as well.
If you already have a Search Console for your original website, you can log in with that account. If you don't have one yet, you can easily create one with your Google account. To gain insight into your clone, simply add a property at the top left. You can use the (sub)domain name or the entire URL of the clone. After this, you will be asked to verify the property. This can be done in several ways, more explanation on this in Search Console.
One of the most useful features of Google Search Console is performance analysis. Performance analysis gives you insight into some very valuable statistics of your search results in Google. For example, how often your search results are clicked, how often the search results are shown to users, and what your average position in Google is. By default, these statistics are shown in a graph that you can filter by, for example, date.
In Google Search console, it is also possible to analyse specific pages within your website. This gives you insight into all the valuable statistics for this page specifically. Of course, not every single page performs equally well. This function is also useful for analysing why a certain page suddenly drops sharply in the organic search results. This is because you will see it immediately if an error has been found.
Setting up a sitemap is very important for the SEO of your website, including your clone. This is because a sitemap gives Google an overview of all pages. Once your sitemap has been created, it is important to pass it on to Google. You do this via the left 'tab' Sitemaps. Then enter the URL of the clone sitemap to add it.
To include URLs of your clone in the Google Index, you can send indexing requests. If you want to see which pages of your site appear in the Google index, you can enter the search query 'site:mywebsite.com' in Google Search. Should there be a URL that is not indexed yet, you can enter this URL at the top of Search Console. When you click enter, on the right it says 'Request indexing'. Clicking this will request the indexing, note that this may take a while.