Which patron saint and the subject of a carol has his saints day on the 28th December?

28th December is the Feast of the Holy Innocents - those babies killed when Herod went on a rampage and massacred any young children and babies who might be Jesus. The Feast of Holy Innocents remembers those babies killed in place of Jesus. I believe you are referring to Good King Wenceslaus but his feast day is on September 28, not December 28. However, there is a well known carol about Good King Wenceslaus "Looking out on the Feast of Stephen" - December 26.