Just picked up this extremely rare coin with a fascinating bit of history behind it!
Maxentius, as Caesar
AE Follis, Carthage Mint
M AVR MAXENTIVS NOB CAES, Laureate bust right
SALVIS AVGG ET CAESS FEL KART, Carthage standing, holding fruits in both hands, H left, Δ in ex.
Rare - 4 examples on ACsearch, 1 on Coinarchives (duplicate), 4 on CNG (one is this coin)
ex. CNG 337/529https://www.cNGCoins.com/Coin.aspx?CoinID=270666
Diocletian's vision for the tetrarchy was a permanent system in which Rome would be ruled by two Augusti and two Caesares in a perpetually peaceful and orderly line of succession - Each Augustus was expected to step down and retire after twenty years in office, and the new Augusti would nominate their own caesares. As Diocletian and Maximian prepared for retirement, everyone knew that Galerius and Constantius would succeed them. As both Maximian and Constantius had adult sons--Maxentius and Constantine, respectively--it was assumed that they would become the new Caesares. This was not the case, however, as Galerius conspired with Diocletian and nominated his own allies - Severus and Maximinus. Constantine and Maxentius were indignant, but did not openly challenge this order of succession. Constantine fled to his father in York in 305 and there won favor with his father and thus all the troops in Britain. When Constantius succumbed to his chronic illness in 306, his troops declared loyalty to Constantine and proclaimed him Augustus. After negotiations with Galerius, Constantine agreed to accept a demotion to the office of Caesar under Severus.
Maxentius would have none of this. All four tetrarchs were too busy to keep an eye on him, so, using the loyalty that the Western troops held for his father, he declared himself emperor from his seat in Rome in October 306. He soon had the backing of his father Maximian, and Carthage followed suit in declaring loyalty. The rest of course, is history.
Enter this coin - Maxentius never once considered himself a Caesar under anyone, so why is he portrayed as such on this coin? The history, if any existed in the first place, was probably destroyed when Constantine took power, but the current scholarly consensus is that Carthage was probably hesitant to be a party to this rebellion, but considered it a safer bet to treat Maximian as the legitimate Augustus, and Maxentius as his Caesar. The rarity of these issues indicates that this discrepancy was quickly set right by agents of Maxentius.
Maxentius' coinage "as caesar" comes only from Carthage, probably only in the last months of 306 or very early 307, and is only of three types:
1) This type of follis as NOB CAES / Carthage Standing
2) An even more rare follis as PRINC INVICT / Africa Standing
3) An equally rare Aureus as NOB CAES / Carthage Standing