What is the value of a 1978 gold penny with fg stamped on it?

There is no gold in any one-cent coins, so what you probably have is a coin that was plated outside of the mint. Another possibility is that it was exposed to heat or some chemical that gave it a golden tone. As such, it's only worth face value.

Assuming you're referring to the tiny letters FG to the side of the Lincoln Memorial on the coin's back, please check your change. ALL cents have those initials; they belong to Frank Gasparro, who designed the reverse side of the coin.