Former Senator John Edwards of North Carolina said Friday that he had an affair in 2006 with a woman who was not his wife. But he denied that he was the father of her baby, who was born in February, about a month after Mr. Edwards dropped out of the race for president. Mr. Edwards, who no longer holds public office, said in a deeply personal statement that he had lied in previously denying the affair and that he was “ashamed” of his conduct. He said that “over the course of several campaigns, I started to believe that I was...