Here we see Darth Vader piloting his fighter while hunting for Rebel starfighters above the Death Star:
He does it in multiple scenes. Was this some sort of targeting configuration controller?
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Judging by the result (a slight adjustment to the targeting grid) it's a fine-tune for the targeting. Think of it as a joystick equivalent of "Shift-arrow" for point-and-shoot games (I'm sure modern fighter planes have something similar but I haven't seen Larian LeQuella around here these parts in a while, sadly).
TIE Advanced x1 (which was Vader's fighter) Wookieepedia page has this to say:
The target tracking system was also more sophisticated than the already formidable advanced targeting system on standard TIE craft, used to overcome the extremely powerful electronic jamming used by all combat craft to defeat target lock in battle. For best performance, the targeting system of the x1 required frequent adjustment in combat.
... but that sentence is completely unreferenced, and therefore probably made up on the basis of A New Hope by whoever wrote the Wikia article in the first place :(
The script describes what Vader was adjusting as his "control stick", "targeting computer", "control lever", and "controls":
Darth Vader calmly adjusts his control stick as the stars whip past in the window above his head.
Darth Vader calmly adjusts his control stick as the stars zoom by.
Vader calmly adjusts his targeting computer and pushes the fire button.
Vader adjusts his control lever and dives on the X-wing fighters.
Vader adjusts his controls and fires laserbolts at two X-wings flying down the trench. He scores a direct hit on Wedge.
Vader adjusts his control stick.
Vader adjusts his control sticks, checking his projected targeting screen.
The most specific of these descriptions is "targeting computer". Also, the last line quoted says that he checked his targeting screen after adjusting his "control sticks", likely because he was expecting a change on the targeting screen due to his adjustment. Therefore, Vader was almost certainly adjusting his targeting computer.
The TIE Fighter Owner's Workshop Manual has a section on the flight controls including a schematic of the yoke and control column. The knob that corresponds to the one that Darth Vader adjusts is for target selection.
OK, hypothetically speaking...
Vader's TIE was an advanced experimental prototype. What if the battle over the death star was one of the, if not the, first time it went into actual combat? Vader did order two pilots to cover him, maybe he was not sure his fighter was fully combat tested yet?
As an experimental unit seeing its first real combat, Vader found in real combat he needed to make some adjustments to deal with real enemies.