A half-month is a common unit of time used in astronomy, used for identifying the time period that objects are first observed when constructing a provisional designation.
Half-months are simple to use: each month is split into two halves, days 1-15, and 16-to-end-of-month. Half months are named with a capital letter, with the first half of January refered to as 'A', the second half 'B'.... all the way through to the second half of December as 'Y'. (But nothing is ever simple; the letter 'I' is skipped, to prevent it being confused with the number 1.)
There is a chance that you have stumbled upon this post in search for the term fortnight