There is no "white transistor". There is a multi-turn trimpot near the upper right corner of the transformer. I don't see any other adjustments, so this probably is the output voltage adjust (as opposed to an output current-limit adjust).
Separate from that, my read of the transformer is that it is capable of supplying 15 Vac at 1 A. There should be plenty of headroom for a 0.5 A output at any voltage below 15 V.
If the trimpot does not have sufficient range, the next step is to post a photo of the underside of the board so we can determine which resistors to change to shift the trimpot adjustment range. That might be difficult, because it looks like the board is supported by grooves in two extrusions. You would have to dismount the main power transistor. Then the board (and the transistor) can slide out of the extrusions with the rear panel wires still attached.
Maybe, two screws release the rear panel from the extrusions, and they drop away. Dismounting the power transistor from the bottom cover lets that drop away, exposing the bottom of the PCB.
Or something like that.