What is the value of a 1878 gem bu Morgan mini gold piece?

Depends on what the coin is made out of.

The coin has absolutely no collector value because it wasn't made by the US Mint. Any value comes from the material the coin was made out of. If the coin was gold plated, it would be worth a couple cents at most. If the coin was solid gold, it would be worth the value of the gold, but no more.