Can it really be a crime to father or have a second child? If it’s your second illegitimate child, and you’re subject to Mississippi law, then yes. As set forth in the Mississippi Code:
SEC. 97-29-11. Illegitimate children; person becoming natural parent of second illegitimate child; jurisdiction.
(1) If any person, who shall have previously become the natural parent of an illegitimate child within or without this state by coition within or without this state, shall again become the natural parent of an illegitimate child born within this state, he or she shall be guilty of a misdemeanor and, upon conviction thereof, shall be punished by imprisonment in the county jail for not less than thirty (30) days nor more than ninety (90) days or by a fine of not more than Two Hundred Fifty Dollars ($250.00), or both. A subsequent conviction hereunder shall be punishable by imprisonment in the county jail for not less than three (3) months nor more than six (6) months or by a fine of not more than Five Hundred Dollars ($500.00), or both. Provided, however, that for the purpose of this section, multiple births shall be construed to be the birth of one (1) child.
(2) The circuit court of the county in which said illegitimate child is born shall have jurisdiction of any action brought under this section. No male person shall be convicted solely on the uncorroborated testimony of the female person giving birth to the child.
Here’s the source.