Actually, I think you were right first time; I read the obverse legend to be "...AVDIVS PF AVG"; Claudius is a better fit than Quintillus.
Reverse type is DIANA LVCIF, Diana the Light-bearer, carrying a long torch. The type is listed in Sear (# 11328) as having officina mark P (= first), struck in Milan mint 269-270 AD.
The same reverse type was issued under Quintillus (Sear #11437) with the same officina mark, mint and date.
Quote:
...on a few occassions, emperors appeared on coinage before they were officially declared an emperor...
Yes, but only when the person in question was an heir-designate or member of the emperor's direct family. Quintillus was the brother of the previous emperor (Claudius II) and wasn't even considered for the purple until his brother unexpectedly died of plague.
Sometimes coinage in the name of a deceased emperor would be struck as a memoriam, but Quintillus was not as highly regarded as his brother by subsequent emperors, so he scored no posthumous coinage.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis