Is there any alternative to download macOS high sierra than App Store? The download link is not allowing me to download high sierra on my MacBook Pro (using Mojave).

From what I've seen Apple is getting more and more restrictive in the availability of previous operating systems. We all should be saving installers as we go. I know I haven't.

You can't open it with Mojave. But you can use the macOS High Sierra installer if it is in your Applications Folder to create a bootable installer.

How to create a bootable installer for macOS - Apple Support

You can also Restart in macOS Recovery and try to install High Sierra from there.

About macOS Recovery - Apple Support

How to reinstall macOS from macOS Recovery - Apple Support

When it says "This copy of the "install macOS" application is too old to be opened on this version of macOS.". It sounds to me like the High Sierra installer must be in your Applications Folder, is it? I am also running Mojave and I tried to download the High Sierra installer and it was downloading OK. It can't be opened with Mojave, but that doesn't mean that the installer is not in your Applications Folder, it just can't be opened with Mojave.

If it is in your Applications Folder, you can still create the bootable installer with it. Make sure to format your install drive MacOS Extended (Journaled) with a GUID Partition Map before you try to create the bootable installer. Name your install drive MyVolume as suggested in the Apple Support Article. Then copy the High Sierra command. Open Terminal and paste the command. Enter your administrative password and Return. Then, type Y when prompted to initiate the creation of your bootable High Sierra installer.

Also, if you should happen to have a Time Machine backup of your system prior to when you installed Mojave you can at least restore from that backup in recovery.