The Quadrans denomination
The quadrans (literally meaning "a quarter") or teruncius ("three unciae") was a low-value Roman bronze coin worth one quarter of an as.

The quadrans was issued from the beginning of cast bronze coins during the Roman Republic with three pellets representing three unciae as a mark of value.

The obverse type, after some early variations, featured the bust of Hercules, while the reverse featured the prow of a galley. Coins with the same value were issued from other cities in Central Italy, using a cast process.
Quadrans
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An AE Quadrans struck After 211 BC in Rome
Obverse: Head of Hercules right, wearing lion's skin headdress; behind, three pellets.

Reverse: Prow of galley right, ROMA above, three pellets below.

Diameter: 20 mm
Die Orientation: -
Weight: 5.79 g
No notes for this coin
Crawford 56/5
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An AE Quadrans struck 81-161 AD in Rome
Obverse: cuirassed and helmeted bust of Mars right

Reverse: cuirass; S__C

Diameter: -
Die Orientation: -
Weight: 2.57 g
(Domitian - Antoninus Pius)
RIC II Anonymous 19
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An AE Quadrans struck AD 81-161 in Rome
Obverse: Helmeted and cuirassed bust of Mars right

Reverse: Cuirass; S-C across fields

Diameter: 16 mm
Die Orientation: 7 H
Weight: 2.74 g
Attributed to the period Domitian - Antoninus Pius. Previously in the collection of John Casey, British archeologist and author.
RIC 19; Sear 2922
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An AE Quadrans struck 161-180 AD in Pannonia
Obverse: laureate and draped female bust right

Reverse: legend within wreath; METAL / AVRELIA / NIS

Diameter: 15 mm
Die Orientation: -
Weight: 2.5 g
No notes for this coin
RIC II 1255; Simic and Vasic, "La Monnaie des Mines Romaines de L
(5) Arse | Saguntum
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An AE Quadrans struck c. 200-150 BC in Arse | Saguntum
Obverse: Shell

Reverse: Dolphin right, crescent above, P (A in iberian script) and three dots below

Diameter: -
Die Orientation: -
Weight: -
No notes for this coin
R&L 153-79; ACIP 1974; SNG BM Spain 1112
(6) Arse | Saguntum
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An AE Quadrans struck c. 200-150 BC in Arse | Saguntum
Obverse: Shell

Reverse: Dolphin right, crescent above, P (A in iberian script) and three dots below

Diameter: -
Die Orientation: -
Weight: -
No notes for this coin
No references provided for this coin
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An AE Quadrans struck ca. 21 BC in Paphos?
Obverse: IMP CAESAR DIVI F, Bare head of Augustus facing right

Reverse: A PLAVTIVS PROCOS, Temple of Aphrodite at Paphos, containing conical xoanon; semicircular courtyard

Diameter: 17 mm
Die Orientation: 12 H
Weight: 4 g
Aulus Plautius as Proconsul of Cilicia et Cyprus

Denomination is probably supposed to be a quadrans given the size and weight per RPC.

The obverse inscription translates to "Commander-in-Chief Caesar, son of the Divine (referring to Julius Caesar)"
The reverse inscription translates to "Aulus Plautius, Proconsul"
RPC I 3906
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An AE Quadrans struck 9 BC in Rome
Obverse: altar; III•VIR•A•A•A•F•F•

Reverse: cornucopiae; LAMIA SILIVS ANNIVS / S__C

Diameter: -
Die Orientation: -
Weight: 2.75 g
Lamia, P. Silius, C. Annius moneyers
RIC I 422
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An AE Quadrans struck 9 BC in Rome
Obverse: LAMIA SILIVS ANNIVS, Clasped hands holding caduceus

Reverse: III VIR AAAFF surrounding large SC

Diameter: 18 mm
Die Orientation: 10 H
Weight: 3 g
L. Aelius Lamia, P. Silius, and C. Annius as moneyers
RIC I (Second Edition) Augustus 420
(10) Augustus
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An AE Quadrans struck 15-10 BC in Lugdunum
Obverse: IMP CAESAR, Head of Augustus facing right, wearing laurel wreath

Reverse: AVGVSTVS, Eagle standing facing with wings spread, head to left

Diameter: 18 mm
Die Orientation: 3 H
Weight: 1.87 g
RPC calls the metal brass
RIC I (Second Edition) Augustus 227, RPC I 508
(11) Brundisium
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An AE Quadrans struck ca. 215 BC in Brundisium
Obverse: Head of Poseidon facing right, wearing laurel wreath, being crowned by Nike at left; trident and 3 dots below

Reverse: Phalanthos, nude, riding dolphin to left, holding large cithara, Nike crowning him; BRVN below; three pellets below

Diameter: 20 mm
Die Orientation: 4 H
Weight: 6.54 g
No notes for this coin
SNG ANS.792
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An AE Quadrans struck 136? (133)BC in Rome
Obverse: head of Hercules right wearing lion skin, club below ●●●

Reverse: prow of galley right ●●● C·NVMITRI ROMA

Diameter: -
Die Orientation: -
Weight: 2.2 g
No notes for this coin
Crawford 246/4a
(13) Castulo
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An AE Quadrans struck c. 120-100 BC in Castulo
Obverse: Diademed head right

Reverse: Boar right, star (comet)* above; KaŚTiLO

Diameter: -
Die Orientation: -
Weight: -
* In 135 BC bright comet appeared and star symbol has appeared on many coins through mediterranean since then.
Villaronga p. 337, 50; SNG BM Spain 1358
(14) Claudius
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An AE Quadrans struck 41 AD in Rome
Obverse: modius; TI CLAVDIVS CAESAR AVG

Reverse: legend around S•C; PON M TR P IMP COS DES IT

Diameter: 0 mm
Die Orientation: 0 H
Weight: 3.12 g

25 Jan - 3 Dec 41 AD

RIC I 84, Cohen I 70, BMCRE I 179, BnF II 185, Hunter I 74, SRCV I 1863
(15) Domitian
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An AE Quadrans struck 84-85 AD in Rome
Obverse: Rhinoceros left

Reverse: S C; IMP DOMIT AVG GERM

Diameter: 0 mm
Die Orientation: 0 H
Weight: 3.2 g

Commemorates colosseum opening

SRCV I 2835; RIC II-1 250; BMC 498
(16) Hadrian
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An AE Quadrans struck 121-122 AD in Rome
Obverse: IMP CAESAR TRAIAN HADRIANVS AVG, Eagle standing facing, head right

Reverse: P M TR P COS III, Winged thunderbolt; SC below

Diameter: 19 mm
Die Orientation: 6 H
Weight: 3.02 g
No notes for this coin
RIC II Hadrian 624
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An AE Quadrans struck 132 BC in Rome
Obverse: Head of Hercules right, wearing lion’s skin; behind, three pellets and below neck truncation club.

Reverse: Prow right; before, three pellets, above M·ABVRI MF / GEM, and below, ROMA.

Diameter: 19 mm
Die Orientation: 0 H
Weight: 8.34 g
No notes for this coin
Crawford 250/2, Sydenham 488, Aburia 7.
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An Aes grave Quadrans struck 225-217 BC in Rome
Obverse: head of Hercules left wearing lion's skin ●●●

Reverse: prow of galley right ●●●

Diameter: -
Die Orientation: -
Weight: 64.8 g
scarce
Crawford 35/4; Thurlow & Vecchi 54; Haeberlin pl. 18, 1-9
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An AE Quadrans struck 211-206 BC in Sardinia?
Obverse: head of Hercules right wearing lion skin; ●●●

Reverse: prow of galley right ROMA; ●●●

Diameter: -
Die Orientation: -
Weight: -
Sardinia, Sicily or south Italy Probably overstrike on Cartaginian Tanit/horse head issue from Sardinia: http://www.ancientcoingallery.net/Files/Images/Coinsite/CoinDB/345_Carthage_horse_head.jpg
Crawford cf. 56/5; RBW 210. Cf.; McCabe H1
(20) Trajan
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An AE Quadrans struck 98-117 AD in Rome
Obverse: IMP CAES NERVA TRAIAN AVG / Laureate bust right, drapery on left shoulder

Reverse: She-wolf standing right, S C in exergue

Diameter: 17 mm
Die Orientation: 0 H
Weight: 3.22 g
No notes for this coin
RIC 692