Regardless of date or mintmark, none of the "State Quarters" struck for circulation have more than face value.
The coin is unlikely to be silver because the only silver State quarters were minted* in San Francisco and sold in special Prestige proof sets. If the coin doesn't display a copper edge it should be examined in person by a numismatic expert, but my guess is that it will turn out to be a plated copper-nickel coin rather than an actual silver quarter. (*) To set things straight, coins are said to be "minted" or "struck". Printing refers to paper and ink.
The Mint has never made gold quarters. If you have a gold quarter then it has been plated which destroys the numismatic value of the coin. Its value is 25 cents plus the value of the little bit of gold they used to plate it. Some chemicals can cause the quarter to turn different colors. This also does not enhance the value of the coin.
....25 cents just like any other post-1965 non-proof quarter. State quarters are not rare or valuable unless they are proof or have some error.
Unless it's a proof or uncirculated coin, it has no added value. All circulation halves made since 1971 are copper-nickel, not silver.
2002
It's just a quarter, spend it.
Copper-nickel, not silver, just like all the other quarters out there in change. Unless it's uncirculated, it's only worth a quarter. A P mint mark, not a "P Mint" - that would be the entire Philadelphia Mint building! The only silver state quarters were issued by the San Francisco mint ("S") and were sold in special "prestige" coin sets. All coins from Philadelphia were made out of copper-nickel.
Not a dime, a nickel. That's why is says FIVE CENTS on the back. (You DID look at the back, right?) Anyway, your coin is only worth 5¢ if it came from pocket change. Billions were minted. The design celebrates the Lewis and Clark expedition. They're not seen much in circulation because people saved them as curiosities.
1803 is the year Ohio became a state. The quarter was minted in 2002, and is worth exactly 25 cents.
Assuming your silver proof quarter does not have any visible nicks or scratches, it is worth $3-$4 -- otherwise it's worth about $1 (Deleted my previous update. Since the S mint mark only appears on proof coins this could not be a circulation strike. The first answer above is correct as it stands.)
If it says CANADA on the other side, 25 cents.
No US quarters were minted in 1812. If your quarter has a picture of George Washington on it, the name "Louisiana", and looks very new that's because it IS new. It's one of the state quarters issued from 1999 to 2008 and is only worth 25¢ Like all of the state quarters in your pocket change it has 2 dates on it. 1812 is the date that Louisiana was admitted to the Union. The actual minting date is 2002 and appears at the bottom of the design.
No, they are worth no more than the metal (or face) value of the coin, the gold plating adds so little gold that it would cost more to de-plate the coin than the gold is worth. For example, a 1965 gold plated half dollar would be worth ~$4.50 in silver scrap just like a normal 1965 half dollar. A 2002 gold plated quarter would be worth just a quarter, just like a normal 2002 quarter.
None of the State Quarters issued for circulation have more than face value.
The U.S. didn't mint any quarters dated 1803. However, if the date 1803 is just below the word "Ohio," and the date 2002 is at the bottom, then it's a modern state quarter worth 25 cents.
1817 is the year Mississippi became a state. The Mississippi state quarter was minted in 2002, and is worth 25 cents.