The simple answer is that any US quarter dated 1964 or earlier is worth many times its face value because these coins were made of 90% silver.
However if a quarter is older than roughly the late 1930s / early 1940s its collector value may be higher than its silver value but that depends on the coin's specific date, condition, and mint mark. For that you have to look at a values guide such as the Red Book, PCGS.com, Numismedia.com, etc.
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All US silver quarters are worth more than face value.
Any quarters minted before 1965 contain 90% silver and are worth several times face value.
None of them quite honestly. The only ones that have value over face are proof coins and error coins. It is possible that state quarters still in mint rolls may be worth a premium to collectors, but unless you have an error coin, you aren't going to find any quarters dated 1965 and later to be worth more than face value.
Regardless of date or mintmark, none of the "State Quarters" struck for circulation have more than face value.
The Mint does not strike gold quarters it's likely been plated and is only worth more than face value to someone who wants it.