How to solve "An error occured while verifying firmware" when updating to Mojave?
I prefer to get my installers from Apple, especially when I get an error with the download like you may have. 


https://support.apple.com/en-us/HT201314


If your Mac is operational, absolutely get a good backup now before you attempt another install. That way you can escalate to an erase install which removes all your existing system and data and ensures if that install fails you know your hardware or network is the cause of the error. 

Since yoU don’t need a backup, I would do the erase install and go to the latest possible. 


https://support.apple.com/en-us/HT204904 (explains how to steer which version installs from recovery)
https://support.apple.com/en-us/HT201255 (explains the overall process)
https://support.apple.com/en-us/HT208496 (erase steps - read last, start here)