What is the value of a 1999 gold US quarter?

There's never been a gold quarter. What you have is a novelty piece made by putting a thin plating of gold (or a golden-colored metal) on a regular quarter. They're sold at inflated prices as "collectibles" on TV and in the backs of some magazines.

Some novelty collectors will pay extra for a full set of plated state quarters in the original packaging from the TV or magazine offer. By itself it's considered to be an altered coin and has no interest to coin collectors.