Did they ever even mention the Beta Quadrant in Voyager?

[Christopher]

The fact you can't produce evidence of what went on there is kind of proof that it got the odd mention but was not part of the narrative really.

The Beta Quadrant includes the entirety of Klingon and Romulan space and half the Federation. Earth spends half of every year in Beta and half in Alpha (which might be part of the point of having the quadrant dividing plane pass through the primary star of the Federation's capital world, to make it more egalitarian). So we've seen a ton of stuff that happened in the Beta Quadrant; it's just irrelevant to talk about quadrant designations in most contexts. After all, you don't see a lot of stories set in England or France where characters talk about which side of the Greenwich Meridian they're on.

 

[AntonyF]

it's just irrelevant to talk about quadrant designations in most contexts.

Ergo it isn't typically addressed.

They talk about quadrants more when it's a counterpoint.

i.e. gamma quadrant - the one all the other side of the wormhole.
delta quadrant - Voyager is lost there.