I've only ever seen this one from Antioch, but given one I assume they all must have been. In particular it seems that all the ~15mm "fractional" under-sized Trier ones are unofficial. Here's a more obvious one that also has a right facing bust (unexpected for the caesars). There's a Celator article by Robert Harlick (referred to by Lars) that illustrates qiute a few of these unofficial Trier ones from the Nether Compton hoard, including this one with a Constantinopolis obverse that therefore has to date to 330+ ! https://community.vcoins.com/thecelator/The-Celator-Vol.21-No.07-Jul-2007.pdf
Thanks for showing this coin. The silvering looks quite strange on the picture, i.e. unlike coins with the usual silverwash of the late 3rd, early 4th century. But of course, it is hard to tell from a picture. Of all the 100 odd Constantinian bronzes in my collection, this is the only one with some original silvering:
I agree it does look a bit odd - unfortunately it's not my coin and I've only got that dealer photo (Holyland) to go by. The appearance of surviving silvering does seem to differ a bit between mints, and even time periods, but unless it's just the lighting that one does seem a bit different than the Antioch campgates that would have been made at the same time.
Unless the catalog description said "full silvering" I would assume that the coin is bronze that for some reason has turned grey.
Actually I tried to find it in Holyland's sold listings to see if there was any mention of the color, but I can't find it. The photo doesn't appear to have been properly lit and/or color corrected since it has an overall cyan shift, which is most obvious in the shadows which ought to be colorless.
There are silver-washed coins from around this time--the one below from A.D. 324-5 is in my collection--but I've never seen one from this anepigraphic series: Cyzicus mint, A.D. 324-325 RIC 155 Obv: CONSTAN-TINVS AVG Rev: PROVIDEN-TIAE AVGG - Campgate with 2 turrets, star above SMKE• in exergue 20 x 18 mm, 2.1 g. I went back and looked at my anepigraphic coin. In indoor light it's very dark, almost black. But in direct sunlight, which is how I photographed it, it's lighter, brighter and shinier. It does not look like bronze, but whether it's an oxidized silver wash or a later, external deposit, I can't say.
Here's a likely imitative Crispus in a similar style to the one @Heliodromus shows. I believe there are no official issues recorded with two stars on the reverse. CRISPUS AE4 (Imitative?). 1.8g, 15.6mm. Trier mint, AD 326. RIC VII Trier 488 var. (one star). O: Laureate, draped and cuirassed bust left. R: CRISPVS / CAESAR / PTR, two stars above.
Thanks, everyone, for this informative thread! I'm glad to know more about my (unremarkable) Constantine example from Antioch.