In Star Trek TOS episodes, interstellar space was divided into large volumes each containing at least several stars. These volumes were identified as sectors and quadrants.
In the TNG era a quadrant became identified as a vast region, a quarter of the entire galactic disc.
Whether sector and quadrant referred to the same type of division or not in a specific work of fiction, they are definitely different words, so the correct answer for sector may not be the correct answer for quadrant.
In any case, TOS was probably not the first space opera to divide interstellar space into quadrants.
In A Life For the Stars James Blish (part of Cities in Flight) 1962, 1963, chapter 4 "Schoolroom in the Sky" Chris deFord is taught galactic history.
In 2289, Earth colonists made contact with a planet of
The Vegan Tyranny, an interstellar culture which, we now know, had ruled most of this quadrant of the galaxy for eight to ten thousand years and was still in the process of expanding.
In 2413, after devastating Vega II, Admiral Alois Hrunta
Led the Third Navy off into an uncharted quadrant with the intention of founding his own interstellar empire.
So are there any earlier uses of quadrants as regions of interstellar space before A Life For the Stars in 1962 & 1963?