Other than esthetics you won't see any difference if the size is close to the same , but off center can be overcome with twin vents , one on either side of the support .
I'm suspecting it would require a very accurate thermometer to determine any difference in attic air temperature at the same elevation anywhere in the attic .I would put it on the sunny side as it heats that side of the roof first and more.
I'd center it. What's your support a flat 2x4?Hi - Does it matter if a gable vent is off center? The truss's I built have a center support which will force me to put the vent on either side of the support. Does it matter ? Thank you