There is a possiblity that an "RCA" unit did exist in Newfoundland after Confederation in 1949. I haven't been able to find a link to a reference but I do recall seeing something a few years ago that suggested the possibilty. It "may" have been on the regiments.org site which is no longer accessible. Therefore, don't hold the following as gospel.
Under the terms of the Newfoundland Act, one of the requirements for the Canadian government was to establish the Newfoundland Regiment as a reserve unit in the Canadian Army (thus making it the only CF unit that would need a constitutional amendment to be disbanded or made inactive). As the majority of Newfoundlanders in the late 40s/early 50s with recent combat experience had served in the artillery, it made sense that some form of artillery unit be established to make use of that experience when the Canadian Militia was started in Nfld. From what I recollect seeing (as noted above), there was formed an element called "166th Field Battery". Whether this was a separate organization badged RCA or was a part of the (Royal) Newfoundland Regiment is unclear. However, at one time (probably in the 50s and 'maybe' in the early 60s) some elements of the regiment did wear a "166th" flash in addition to the Royal Newfoundland Regiment Canada shoulder badge on their battledress. The designation 166th was to be in honour (continuation) of the 166th (Newfoundland) Field Regiment RA. I have been told that a photo showing such a flash maybe in a book titled Better Than The Best, The Story of the Royal Newfoundland Regiment 1795 -1995, Facey-Crowther, David ed.; I haven't had the opportunity to find this book yet to confirm.
One of the things said about the R NFLD R was that it was the only infantry unit with its own artillery so if this had been formed as an independant battery it was probably quickly incorporated into the R NFLD R. My uncle once remarked to me after I joined the army (in the 70s) that he had been in the Militia as a gunner(?) for a couple of years around the time he was in his late teens or shortly after; that would make it around 1950. Unfortunately he is no longer available for me to query but I do remember him being very specific that he had not been in the R NFLD R.