The Questions of Bartholomew are a once-widespread text, written between the first and fifth centuries in Greek, mostly likely in Egypt. It has surviving copies in Slavonic, Coptic, Latin, and Greek, and was the basis for a medieval Latin Church sermon. Fr. K. Parhomenko suggested it as a source for the discussions in the Orthodox Church's hymnography between people in Hades in connection with Christ's descent there.
The most confusing part for me in the Questions of Bartholomew is Jesus' reference in Chapter VI to the 12 heads of God. M.R. James' translation of Jesus' words to Bartholomew goes:
5. Woe unto him that sweareth by the head of God, yea woe (?) to him that sweareth falsely by him truly. For there are twelve heads of God the most high: for he is the truth, and in him is no lie, neither forswearing.
A Russian translation that probably uses different manuscripts, and which I have translated into English goes:
Alas, woe to the one who swears by the head of God, even if he doesn't swear a lie, but speaks the truth. For the High God has 12 heads. And He Himself is the Truth and there is no lie in Him and no oath-breaking. He descends and reveals to the whole world the Word of Truth.
The passage relates to Matthew 5:34-36, in which Jesus says: "But I say unto you, Swear not at all; neither by heaven; for it is God's throne: Nor by the earth; for it is his footstool: neither by Jerusalem; for it is the city of the great King. Neither shalt thou swear by thy head, because thou canst not make one hair white or black."
In ancient Apocalyptic literature, "heads" sometimes was a symbol for kingdoms, kings, or leaders. For example, in Daniel 7 a beast has four heads (eg. for the four kingdoms of Alexander the Great's empire), and in Revelation 13, the beast coming out of the sea has 7 heads.
Ancient Israel was made of 12 tribes that could be ascribed to 12 "heads" or forefathers, such as Judah, Benjamin and Reuben. Christ named 12 apostles to head the Church, which in different senses was considered Christ's "body" and the "New Israel".
In his essay "Jesus and the Twelve", Scot McKnight writes that in the Old Testament,
the predominant use of "twelve" is for the sons of Jacob / Israel ([Genesis] 35:22-26; Sir 44:23-45:1). The sense of the "twelve sons of Israel" as heads of the twelve tribes moves from a physical literality (the actual sons of Israel and a real tribal interest; see Gen 42:13, 32; 49:28; Tob 1:4; 4:12; 5:9-14; Add Esth 14:5) to a representation for the descendants (the twelve tribes) and hereditary representatives (twelve tribal princes/chieftains, and so on). So: Moses sets up an altar at the foot of Sinai with twelve pillars "for the twelve tribes of Israel" (Exod 24:4); Moses finds "chieftains" and "heads" (Num 1:5-16) who will help him take a census of the whole house of Israel (see 1:44); Moses sends twelve to reconnoiter the land that was promised to Israel (Deut 1:22-23); and upon entry into the land beyond the Jordan and after its reconstitution, the "twelve" play a major role (see Josh 4:2, 3, 8, 9, 20; 18:24; 19:15; 21:7, 40).
So my guess is that since "heads" commonly refers to kingdoms or leaders, and the hostile heads of the beasts in Daniel and Revelation refer to hostile foreign kingdoms or rulers, then the 12 "heads" of God would refer to kingdoms or rulers belonging to God. Since the heads of Israel are twelve patriarchs, and the 12 apostles were heads of the Church, Christ's "body", then the 12 apostles would metaphorically or spiritually be "heads" of Christ's "body", the Church. In Matthew 5, on which the passage in question must be based, Jesus tells the 12 apostles not to swear by their heads. A rule directed to the 12 apostles against swearing by their heads would fit with a rule against swearing by God's head that is justified by the concept of God having twelve "heads" (the apostles).