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There is an application named DesignPad released by Quark for iPad (there is none for iPhone). See here --> https://itunes.apple.com/us/app/quark-designpad/id551786067?mt=8
Also see here --> http://www.quark.com/Products/DesignPad/
You will be able to create QuarkXpress files with it on your iPad and transfer it to your Mac.
If you have any questions or would like any additional information, please don't hesitate to ask.
Remember, this is not my final answer. If my solutions didn't work please don't rate me bad or poor. Instead please reply back to me and I will continue to help you until we fix the problem or you are satisfied.
DesignPad is not a substitute for the computer version of QuarkXpress. It have a limited functionality and it will allow you to create simple Quark files on the go.
I've not personally used that application, but we can check whether it support computer Quark files. Open App Store and download the application. It is free.
Then connect the iPad to your Mac and transfer the Quark files to the DesignPad using iTunes File sharing feature. See here --> https://support.apple.com/en-in/HT201301
Let me know once you did that, so we can move to next step.
You're most welcome Gary. I will be here if you need any assistance