How to Convert Quark to InDesign

If you only have a file or two to convert, you can instead try markzware's online conversion service. I've used it for the odd Publisher conversion and it was very good for a relatively small charge. That would be cheaper than buying the plugin or their other standalone conversion products, but if you have a lot, the plugin is well worth the money in time saved.

https://helpx.adobe.com/indesign/using/converting-quarkxpress-pagemaker-documents.html

In the early days of InDesign, I mean early (InDesign 2 through I think InDesign CS6), InDesign could open QuarkXPress 3.3 and 4 documents and templates. I co-wrote a book with David Blatner introducing InDesign to QuarkXPress users. But unless you have a copy of InDesign CS6, and you have some old XPress 3.3. and 4 documents hanging around it wouldn't work for you!