You can run VCMI on iOS 12.0 and later, all devices are supported. If you wish to run on iOS 10 or 11, you should build from source, see How to build VCMI (iOS).
To run on a non-jailbroken device you need to sign the IPA file, you have the following options:
your.bundle.id with something like com.MY-NAME.vcmi. After that use the above signer tool.To install the signed ipa on your device, you can use Xcode or Apple Configurator (available on the Mac App Store for free). The latter also allows installing ipa from the command line, here's an example that assumes you have only 1 device connected to your Mac and the signed ipa is on your desktop:
/Applications/Apple\ Configurator.app/Contents/MacOS/cfgutil install-app ~/Desktop/vcmi.ipa
Note: if you don't need in-game videos, you can omit downloading/copying file VIDEO.VID from data folder - it will save your time and space. The same applies to the Mp3 directory.
If you bought HoMM3 on GOG, you can download the files directly from the browser and install them in the launcher. Select the .bin file first, then the .exe file. This may take a few seconds. Please be patient.
To play the game, you need to upload HoMM3 data files - Data, Maps and Mp3 directories - to the device. Use Finder (or iTunes, if you're on Windows or your macOS is 10.14 or earlier) for that. You can also add various mods by uploading Mods directory. Follow official Apple guide and place files into VCMI app. Unfortunately, Finder doesn't display copy progress, give it about 10 minutes to finish.
If you have data somewhere on device or in shared folder or you have downloaded it, you can copy it directly on your iPhone/iPad using Files application.
Place Data, Maps and Mp3 folders into vcmi application - it will be visible in Files along with other applications' folders.
You can also upload files with Xcode. You need to prepare "container" for that.
You can start game directly (avoiding the launcher) by changing setting in iOS Settings app - VCMI.