The original IRT I believe had their own security as did the BRT/BMT ( note if you read accounts if the early subway, guards were not security per se, they were what we call conductors). I believe the IND had it's own police force and when the city took over the subways in the 40s, they merged to form the TA police that be became the NYC transit police. They used to be independent, they merged with the NYPD a number of years ago, now it is a branch of NYPD.
Or at least that is what I know of it. On the first subway ride in 1904 after system was opened, someone had a diamond stickpin stolen.