The Quarter-follis denomination
The quarter-follis - ancient name unknown - was a Roman bronze denomination struck ca. 294-315. It was the smallest fraction struck during the Tetrarchy.

The weights varied from slightly less than one gram to almost three grams, but most seem to be centered around one scripulum, a Roman measure of weight which equals 1.13 grams. A distinction between quarter-folles and "denarii communes" may not exist, but the term "Quarter-Follis" is the most commonly used. Since the follis (q.v.) was first struck at between 8.5 and 11.0 grams, it is uncertain that a fractional quarter was meant. After the follis was reduced in weight the ratio comes closer, but still is hardly exact.

They were only intermittently issued during the period and were never common, judging from their scarcity today.
Quarter-follis

(1) Anonymous | Maximinus II 312 AD
Obverse: turreted and veiled Tyche of Antioch seated on rocks, holding grains; river-god Orontes, standing facing in waist deep water, arms outstretched; GENIO AN_TIOCHENI
Reverse: Apollo standing left, holding patera and kithara; APOLLONI__SANCTO / B / SMA
Ref: McAlee 170(b), Van Heesch 3(a), Vag...
(2) Anonymous | Maximinus II 312 AD
Obverse: turreted and veiled Tyche of Antioch seated on rocks, holding grains; river-god Orontes, standing facing in waist deep water, arms outstretched; GENIO AN_TIOCHENI
Reverse: Apollo standing left, holding patera and kithara; APOLLONI__SANCTO / I / SMA
Ref: McAlee 170(i), Van Heesch 3(a), Vag...
(3) Constantius I 305-306 A.D.
Obverse: CONSTANTIVS AVG, laureate head right.
Reverse: GENIO POP-VLI ROMANI, Genius standing left, holding patera and cornucopiae
Ref: RIC VI Siscia 169a
(4) Severus II 305-306 AD
Obverse: laureate head right; SEVERVS NOB C
Reverse: Genius standing left, wearing chalmys and modius, holding cornucopia, pouring libations from patera; GENIO POP_VLI ROMANI / SIS
Ref: RIC VI Siscia 171a
(5) Severus II 305-306 AD
Obverse: FL VAL SEVERVS NOB C, Head of Severus facing right, wearing laurel wreath
Reverse: GENIO POPVLI ROMANI, Genius standing facing left, nude except for chlamys over left shoulder, holding cornucopia and patera; SIS in exergue
Ref: RIC VI Siscia 170a