This article examines the practice of fasting on the Sabbath found among Roman Christians, Marcionites and Roman Jews alike. The conclusion is that Roman Christian fasting was derived from the historic practice of Roman Jewish circles (in which fasting on the Sabbath was an established custom), although the aricle notes:
the explanation given in the eleventh century by Humbert, which certainly sounds Marcionite, is accepted by [Markus] Vinzent as the true rationale, and on this basis he suggests that Sabbath fasting is a Marcionite innovation which was adopted within wider Roman Christianity under Marcion's influence (Vinzent, “Marcion's Roman liturgical traditions”, 191-195).
The author, Alistair C Stewart, challenges this (see below).
It seems Christians outside Rome considered fasting on the Sabbath a heresy.
Thus the ps-Athanasian fourth-century Syntagma Doctrinae instruct[ed] ascetics: “And do not allow any Marcionites, or another heresy, to lead you astray, into private fasting on the Sabbath or on Sunday,” and the closely related Fides patrum similarly state[ed] “And lest any Marcionites, or another heresy, lead you astray into fasting on the Sabbath, do not neglect the meetings.
The origin of the Marcionite practice itself is uncertain, although the influence of Jews in Pontus is considered likely.
The author, Alistair C Stewart, notes later
... the Marcionites, following a practice of emerging Judaism, kept a meal of fish on Friday evening intended to convey a state of purity. Thus I suggest that the following day was kept fasting in order to maintain that purity for the study of Scripture, which was the fundamental purpose of early Christian (and Jewish) Sabbath-keeping. It is possible that this Marcionite practice is derived from the Jewish practice of Pontus; unfortunately we are here at the limit of our knowledge.
This leads us to examine the origin of the wider Roman practice which, as has already been seen, Vinzent attributes to Marcionite innovation. The occurrence of a cena pura in Marcionite circles, however, indicates that tthe] Roman Christian practice cannot have derived from that of Marcion; or indeed that that of Marcion might be derived from wider Roman Christian practice, as the Roman (non-Marcionite) Christian practice is distinct from that of Marcionites in that the [Roman Christian] fast is not disrupted by the cena pura on Friday evening.
Rather the days are seen by Innocent I as fasting days on the model of the fasts of Good Friday and Holy Saturday; that is to say there is an uninterrupted fast from Friday to the end of Saturday, and so there is a significant difference between the two Roman Christian fasting practices. Although Innocent explains the nature of the fast with reference to the paschal fast, we cannot deduce the historical origin of the Sabbath fast from his comments; his explanation is certainly secondary, as such an imitative practice could not have come about in Rome until the beginning of the third century, since prior to this date Rome was divided between those who were Quartodeciman and those who knew no paschal celebration.
An indication of the antiquity of this practice is the absence of any record of the introduction of this practice into Roman Christianity ...
And he notes that Epiphanius stated that Marcionites fasted on the Sabbath
for the following reason: “Since it is the rest of the God of the Jews who made the world and rested the seventh day, let us fast on this day, so as to do nothing congenial to the God of the Jews” (Panarion 42.3.4)