1966 No Mint Mark Quarters were minted at the Philadelphia Mint. They didn't use a Mint Mark back then.. Worth 25 Cents
All of the coins in 1965 1966 and 1967 don't have mint marks. And this 1966 quarter may or may not have been produced at Philly. Since the other mints were operating and making no mint mark coins during those 3 years.
You would need to post picture, both front and back, clear & cropped so we can decide if you have a off center or possible misaligned die.
Actually quarters for 1965, 1966, and 1967 were minted at all three mints, without mintmarks. It was a special change to the law, to mint enough coins to replace the silver dimes and quarters that were being withdrawn. Silver 1964 quarters were minted up to April 1965 as part of the same program. Total mintages... 1965 - 1.8B 1966 - 821M 1967 - 1.5B
The mint system did away with mint marks on coins to discourage collectors from hoarding them. In the mid 1960s, coin collectors were the #1 public enemy in the eyes of mint and other government officials. There was even a bill proposed by a Senator from Nevada named Bible that would have put the coin collector industry pretty much out of business. The real problem was the fact that silver prices were about the reach the “magic number” of $1.29 an ounce where the face value equaled the melt value for silver coins. Some dealers, collectors and coin hoarders anticipated this and were hoarding and buying up 90% silver coins at nominal amounts over their face value. I knew one Philadelphia dealer who was paying 8% over face in 1968-9.