The crossword solution for the term 'prefix with DAY' is MID. The prefix 'MID' is derived from the Old English word 'midd', meaning middle. It is commonly used to refer to something that is in the middle of two other things, or halfway between two points. It is also used to refer to something that is in the middle of a period of time, such as MID-morning or MID-afternoon. When combined with the word 'DAY', it can refer to the middle of the DAY, or noon.