It completely depends on the data you are serving to users, let suppose if you're offering them to download simple PDFs/Word Docs/Spreadsheets, then user should be allowed to download that data, as per emerging UI Trends- all the applications are being designed n developed with Mobile-First view, so that not much functionalities are being compromised on mobile devices.

In case, you still want to restrict user to download that on small devices, you can better do a Popup/Tooltip thing - showing a regret message to the user.

Also if you use a small Popup on click of those downloadable buttons, there you can give a handy checkbox to user if he want to proceed all the downloads on same device or would like to switch to the desktop version of the app later.

That way the control will always be there in user's hands, which is the need of an hour. ;)

It completely depends on the data you are serving to users. Let's suppose you're offering them to download simple PDFs/Word Docs/Spreadsheets – then the user should be allowed to download that data, as per emerging UI Trends- all the applications are being designed and developed with Mobile-First view, so that not too many functionalities are being compromised on mobile devices.

In case, you still want to restrict the user to download the file on small screen devices, I would recommend to use a Popup/Modal Window or Tooltip - showing a regret message to the user.

Also if you use a small Popup on click of those downloadable buttons, you can offer a handy checkbox to the user to check if he/she wants to proceed all the downloads on same device – or would instead prefer to switch to the desktop version of the app later.

That way the control will always be there in user's hands, which is the need of an hour. ;)