Here’s Wikipedia’s take on its history:
The story goes that Screech was first created in the days of the Triangle Trade, where the same barrels were used to carry molasses and rum, and only occasionally cleaned. The barrels built up a deposit of impossibly sweet sediment at the bottom, which was melted out with boiling water and either fermented or mixed with grain alcohol. This concoction eventually became known as screech.
The Screech sold legally in liquor stores both in and outside of Newfoundland is blended and bottled by the Newfoundland and Labrador Liquor Corporation, which unlike its counterparts in other provinces has retained its bottling business (apparently so it can carefully control the quality of a product so closely identified with the province). However, consumers should be aware many Newfoundlanders do not view the NLC-bottled Screech as the genuine article, as stronger Screech that cannot be legally sold continues to be blended and distributed in an extra-legal manner.