This copy of the Install macOS Mojave application is damaged: Even After Correcting Time
I had this problem and tried many things.  system date was correct.  But only one website help me to fix this problem. Simple method and works on all version of macOS installation. I suggest to try this method. Because it works for me. 
https://www.computertipslaiju.com/2019/10/this-copy-of-install-macos-mojave.html

Added by barlop

The method at that link says

Disconnect wifi, then change the date, use the form mmddhhmmyyyy e.g. 042412302016

sudo date 042412302016

You need to disconnect wifi so the date won't automatically change.

The year makes all the difference.  For me, my year was set to the current year 2020 and I got that error trying to install High Sierra from https://support.apple.com/en-us/HT208969 

By changing the year of my system's date to 2016, I was able to start the installation.

For another person https://www.youtube.com/watch?v=t8RRm5N_n8s their year was some old date of 2001. Similarly, changing to 2016 made it work without that error.