The two coins illustrated were acquired together, and both appear to be ancient imitations over-struck on genuine coins
1. Obv. CONSTN - INVS AVV, reversed N’s, bare head of Constantine I right, over-struck on an IOVI [CONSERVATORI] coin struck in Heraclea, with SMH (gamma) visible below the bust, and IOVI behind the bust
Rev. CNONSTANTIVAX, reversed Ns (for DN CONSTANTINI MAX AVG), [N]OB C also visible at approximately 5.00, all around VOT XX within wreath, TP in exergue
Weight 2.42 grams
Undertype presumably one either RIC Heraclea 53 54 or 55, as these are the only IOVI coins struck in the name of the Caesars Crispus, Licinius II and Constantine II at Heraclea
2. Obv. CONSTANTINVS P AVG with under type bust clearly visible
Rev. DN CONSTA[N]TINI (CTO COMI), around VOT XX within wreath, PT[R?] in exergue, over-struck on a SOLI INVICTO type per visible legend and vestiges of the head of Sol and globe in left hand also visible
Weight 3.18 grams
Coin 1 is clearly imitative, given the blundered legends and reversed Ns on both dies, as well as the mis-alignment of the Xs in the reverse wreath
Coin 2 is less obviously imitative, and I initially identified it as RIC Trier 439, however, the final R is not clear, and as with coin 1, the Xs within the wreath are quite poorly aligned, suggestive of an imitation.
Interestingly, RIC 439 is listed as R5, and could be considered an anomaly within the series, which has Constantine issuing the SARMATIA DEVICTA reverse type in large quantities (RIC 435, rated C3 in both officina), with the predominant issue for the Caesars Crispus and Constantine II being the VOT X in wreath types (RIC 440, 441, both rated C3 in both officina. (As with Constantine’s R5 wreath type, there are similarly rare SARMATIA DEVICTA reverses known for Crispus and Constantine II,RIC 436-38). It would be useful to check whether the example of RIC 439 in the Fitzwilliam cited by RIC is of good style or not; while their website includes coins in their on-line database, I wasn't able to locate this coin
I am intrigued as to why a counterfeiter would overstrike seemingly official coins, and was wondering whether anyone has seen anything similar or knows of any references that discuss this phenomenon. The weights seem normal for the under types and neither coin shows any obvious signs of clipping. Perhaps coins of the Licinnii that had been demonetised ?