new ceiling fixture
If I understand correctly, you find a wire in the middle of the ceiling, which has power, but currently not being used....
if this is the case, you need to install a switch to make this powered wire being able to control by the switch.
so you need to do some fishing in the wall from the attic, that is doable, you need to have very long and thick drill bits to drill a hole on the wood plate then drop the wire to form the switch, I done that for my cable TV, it is easier than it described.
anyhow, once done that, everything else should be easy, just how to put connection together... but before going further... please let us know if this is the situation ....