There does seem to be clear evidence that beeswax and soy wax burns cleaner than paraffin, that is, they produces less soot and volatile organic compounds (VOCs) (Rezaei et al). So it could be argued that compared to burning paraffin in your living space 24/7, using beeswax would improve air quality, but I don't think that's the argument being made when a website says, "When beeswax candles burn, they clean the air like a great, natural, air purifier." Ebeehoney
The method of "purification" is not always mentioned, although a few sites mention negative ions. It's unclear to me why beeswax would produce more negative ions than paraffin, and the only ion measurements that I was able to find on google scholar were for paraffin wax (Wright et al). In fact, this paper made it clear that ions are associated with soot, so my conclusion would be candles that soot more (i.e. paraffin) should have more negative ions.
Is there any basis to the claim that beewax candles purify the air?