If it is a "s" quarter it will always have the S mintmark. You can find this mintmark usually on the back of the coin. The exact location will depend on the type of quarter.
It would be located on the right of the quarter on the observe nest to the ponytail.
If there is no mintmark under the eagle on a quarter then the coin was minted at the Philadelphia Mint. That's the only mintmark position for Washington quarters dated 1964 and earlier. The mintmark was first put on the front of the coin in 1968.
Which one? A date and mintmark please:
If you mean a 1966 American quarter, then none.
The mintmark is a "D" not a "P" and it's just a quarter.
Zero. A 1966 U.S. quarter is 0% silver.
It would be located below the wreath on the back(tail) of the coin.
If you mean a mintmark? No US coins made in 1965, 1966, and 1967 have any mintmarks.
If you mean it has no Mintmark, value depends on the year it was struck.
If it has a mintmark its on the reverse under the wreath, it can only be a D or S.
If it has the D mintmark it means it was made at the Denver mint. If it has the S mintmark it means it was made at the San Francisco mint.