What do the initials FJG stand for in my 10k white gold ring?

The initials "FJG" in your 10k white gold ring likely stand for the initials of the jeweler or manufacturer who created the piece. It's not uncommon for jewelers to engrave their initials or a hallmark to indicate authenticity and craftsmanship. To get specific information about the maker, you may want to consult a local jeweler or appraiser who can help identify the brand or designer associated with those initials.