Serapis (Egyptian and Greek)
A god Serapis is was a state god, formulated by Ptolemy I (305BC), conceived as a synretism of the the bull shaped god Apis and Osiris, the judge of the afterlife, worshiped from 305BC to 100AD.
In religio-mythology, Serapis, aka “Aser-hapi”, a Greco-Roman-Egyptian god syncretism of the Egyptian gods Osiris, i.e. the moral judge of the soul in the afterlife, and Apis (or Hapis) (Ѻ), i.e. the son of Hathor (or Isis), considered the living personification of Ptah in Memphis (Jordan, 1993), therein becoming the joint god “Osiris-Apis” (compare: Lazarus; Raising of Lazarus), a state-promoted supreme male god, whose worship peaked as chief male god (see: supreme god timeline) during the Greco-Roman period, from the rule of Ptolemy I (305BC) to Vespasian (69AD), the attributes of which were said to be equivalent of the highly popular Apis, the said intermediary between the supreme god (Ptah) and mankind, PLUS Osiris in full (rather than just his Ka or life force). [1]

Overview
Under Ptolemy I Soter (305BC), efforts were made to integrate Egyptian religion with that of their Hellenic rulers. Ptolemy's policy was to find a deity that should win the reverence alike of both groups, despite the curses of the Egyptian priests against the gods of the previous foreign rulers (e.g. Set, who was lauded by the Hyksos).

Alexander the Great (332BC), previous to Ptolemy I, had attempted to use Amun for this purpose, but he was more prominent in Upper Egypt, and not as popular with those in Lower Egypt, where the Greeks had stronger influence. The Greeks had little respect for animal-headed figures (e.g. the bull-headed Apis), and so a Greek-style anthropomorphic statue was chosen as the idol, and proclaimed as the equivalent of the highly popular Apis. This new syncretistic god was named Aser-hapi (i.e. Osiris-Apis), similar to the latter La-Azarus becoming the man "Lazarus", which became Serapis. His most renowned temple was the Serapeum of Alexandria.
Serapis (Gibbon, 1883)
A sketch of Serapis from Edward Gibbon (1883). [4]

In 146AD, emperor Antonius Pius, according to Edward Gibbon (1883), introduced the worship of Serapis in Rome and had the “mysteries” celebrated on May 6th. [4]

In 1883, Edward Gibbon recounts the overlap of Serapis worship and Christianity as follows: [4]

The engraving of Serapis shown on the preceding page (adjacent), represents the god grasping in his left hand the tail of a huge serpent, which is entwined around his body, while the head appears at his feet. Between the folds of the reptile are seen figures of men and various animals, the symbolical meaning [Zodiac symbols] of which can only be conjectured. Like all the images of Serapis, the countenance has the stern aspect of Jupiter, and the head is surmounted with the calathus or basket peculiar to this Egyptian deity.

In The Diegesis (pg. 204), Robert Taylor quotes from Socrat. Eccl Hist. lib. 5. c. 17. as follows:

"In the temple of Serapis, now overthrown and rifled throughout, there were found engraven in the stones certain letters which they call hieroglyphical; the manner of their engraving resembled the form of the cross. The which, when both Christians and Ethnics beheld before them, every one applied them to his proper religion. The Christians affirmed that the Cross was a sign or token of the passion of Christ [see: Passion of Osiris], and the proper symbol of their profession. The Ethnics avouched that therein was contained something in common, belonging as well to Serapis as to Christ; and that the sign of the cross signified one thing unto the Ethnics, and another to the Christians. While they contended thus about the meaning of these hieroglyphical letters, many of the Ethnics became Christians, for they perceived at length the sense and meaning of those letters, and that they prognosticated salvation and ‘life to come’."

"This most important evidence," continues Taylor, "of the utter indifference between Christianity and ancient Paganism, is supplied by a Christian historian; and independent of its fairness, as taken from such a source, and its inherent verisimililude.it is corroborated by a parallel passage from the ecclesiastical history of Sozomenes, who, about the year 443, wrote the history of the church from the reign of Constantine the Great to that of the younger Theodosius. He is speaking of the temple of the god Serapis:—' It is reported that when this temple was destroyed, there appealed some of those characters called hieroglyphics surrounding the sign of the cross, in engraven stones ; and that, by the skillful in these matters, these hieroglyphics were held to have signified this inscription—This Life To Come! And this became a pretence for becoming Christians to many of the Grecians, because there were even other letters which signified this sacred end when this character appeared.'"

The charge of Serapidolatry, or the worship of the god Serapis, was brought against the primitive Christians, by no vulgar accuser, no bigoted intolerant reviler, but by that philosophic and truth-respecting witness, the emperor Adrian. In a certain letter which he writes, while in the course of his travels, to the Consul Servianus, he slates, that he found the worshipers of the god Serapis in that country distinguished by the name of Christians. ‘Those,’ he says, ‘who worship Serapis, are Christians; and those who are especially consecrated to Serapis, call themselves the bishops of Christ.’ In relief of which charge, the learned Kortholt, from whose valuable work, the Paganus Obtrectator, I have taken this passage, pleads, and indeed it might be so, that when this emperor was in Egypt, some of the Christians, actuated by fear, concealing their true religion for a season, might have held out an appearance of having embraced the superstition of the Pagans. Thus, in the Ancient Martyrology, in the history of Epicharmus. an Egyptian martyr, it is related that all the Christians in Alexandria, upon the coming of a cruel judge, either fled away, or pretended to be still followers of the Pagan impiety: and if the approach of a judge only could produce this effect, it is no wonder that the coming of the emperor himself, and he, as they all knew, being a most strenuous asserter of the Gentile superstitions, should have a similar effect."

Gibbon concludes this by quoting a bit from Samuel Dunlap on the late origin of the name Christianity.

Quotes
The following are related quotes:

“Ye priests! who murmur at this relation, you wear his emblems all over your bodies; your tonsure is the disk of the sun; your stole is his zodiac; your rosaries are symbols of the stars and planets. Ye pontiffs and prelates! your mitre, your crozier, your mantle are those of Osiris; and that cross whose mystery you extol without comprehending it, is the cross of Serapis, traced by the hands of Egyptian priests on the plan of the figurative world; which, passing through the equinoxes and the tropics, became the emblem of the future life and of the resurrection, because it touched the gates of ivory and of horn, through which the soul passed to heaven.”
Constantin Volney (1791), The Ruins (§XXII: Origin and Filiation of Religious Ideas)

“Apollodorus identifies the Argive Apis with the Egyptian bull Apis, who was in turn identified with Serapis (Sarapis). Pausanias [c.160AD] also conflates Serapis and Egyptian Apis: ‘Of the Egyptian sanctuaries of Serapis the most famous is at Alexandria, the oldest at Memphis. Into this neither stranger nor priest may enter, until they bury Apis’.”
James Frazer (1913), Note to the Biblioteca of Pseudo-Apollodorus [2]

“The cult of Serapis and Isis was introduced into Greece in the fourth century [BC] and into Italy by the later second century.”
Patrick Walsh (1997), notes to Cicero’s On the Nature of the Gods [3]

References
1. (a) Budge, Wallis. (1904). The Gods of the Egyptians, Volume Two (Vespasian, pg. 217; Serapis, pg. 349) (Ѻ). Dover, 1969.
2. (a) Pausanias. (c.160AD). Description of Greece (1.18.4). Publisher.
(b) Pausanias (geographer) – Wikipedia.
(c) Frazer, James. (1913). Note to the Biblioteca of Pseudo-Apollodorus (2.1.1) (Ѻ). Loeb Library Classics.
3. Cicero. (45BC). The Nature of the Gods (Introduction, translation, and notes: Patrick Walsh) (pg. 201). Oxford University Press, 1998.
4. Gibbon, Edward. (1883). History of Christianity: Comprising All that Relates to the Progress of the Christian Religion in "The History of the Decline and Fall of the Roman Empire," and A Vindication of Some Passages in the 15th and 16th Chapters (Serapis, pgs. 526-27). P. Eckler.

External links
Serapis – Wikipedia.

TDics icon ns