What is a case where the police obtained a false confession, and the conviction was eventually overturned, based on other evidence, such as DNA?
Perhaps the most famous case in which confessions that turned out to be false were used to convict people was the case of the "Central Park Jogger." This was a case in which a woman raped and badly beaten while jogging in Central Park in New York City. The crime occurred in 1989. Five young men were convicted based largely on their confessions.
In 2002, their convictions were overturned. This happened in part because of DNA testing. The DNA found at the crime scene did not match the youths who were convicted. Later, another man confessed to the crime and the DNA did match him. For that reason, the convictions were vacated.