You can't get any more vague...
I would like to manufacture a case a little larger than a glasses case.
It needs to be insulated with aerogel - and I need to keep the case cooled for 24 hrs with ordinary refrigerator temperature, possible USB connectivity for further cooling.
Any cooling/compression advice on cooling capabilities this size?
I agree with Cragyon, this isn't very much information...
As far as cooling goes, refrigeration is basically a heat pump, there are small units on the market but likely not small enough to suffice what you may be looking for, especially if it may be USB powered. And why do you need aerogel? It is a good insulator but costly for your needs. It isn't inherently cooler or something like that.
More info is needed.