The chances for conceiving on the 6th day of the cycle are possible only if your cycle lasts no more than 21 day which is a very rare case. 21 days is the shortest normal duration of a menstrual cycle. A menstrual cycle shorter than 21 days is considered abnormal. Therefore, it's highly unlikely that the father of your child was "the other guy". Nonetheless, the only way to be sure is to request a paternity test from both of the men.