What you have is most likely a "lamination error". If so, it could retail for about $10 but it would need to be evaluated in person by a dealer or appraiser who works with error coins.
Current US dimes, quarters, and half dollars have two outer layers of cupronickel cladding* bonded to a copper core. Blanks for the coins are punched out of large rolls of metal stock. Sometimes the ends of the rolls aren't properly clad and one or both sides may be missing from the copper core.
* "Plating" is normally a thin coat of metal applied electrically or chemically in a liquid bath. Cladding for coins is much thicker and is bonded mechanically.
The gold plating adds nothing to the value of 25 cents, unless you find someone that wants it, it's a quarter.
25 cents if the quarter was made in 1965 or later. Gold plating really adds nothing to the value of a coin and is considered to be damage to a collector. While interesting, the amount of gold used in gold plating is too small to be stripped off and sold and make a profit. However, if the quarter is dated 1964 or earlier, it is a 90% silver quarter and is worth about $6.25 for the silver content in the quarter, but the gold adds nothing to the value.
A 2008 gold plated quarter only has value to someone who wants it. The plating does not add to the value of the coin in any way at all. But it's still 25 cents.
It's a novelty item worth couple of cents for the gold plating plus whatever the underlying quarter is worth. If the quarter is copper-nickel, then it's only worth a quarter. If it's a special silver "prestige" quarter made in San Francisco it's at least worth maybe $3.50 for its metal content.
Most Bicentennial quarters are worth at least $5 in Mint State. Any piece in circulated condition is generally only worth its face value. In other words, 25 cents. Bicentennial quarters were made to commemorate America's 200th birthday.
July 24, 2009 Gold plating a coin destroys its numismatic value. The Bicentennial quarter is worth but a quarter plus the value of the bit of gold used to plate it.
$25
How much is a bicentennial 1776-1976 quarter dollar worth
¢.25
Jack L. Ahr.
$ 7.93
It would be located on the right of the quarter on the observe nest to the ponytail.
It's just a Bicentennial quarter, spend it.
25 cents.
25 cents
25 cents.
25 cents.