Doing a cross-reference study on “so-called” led to a renewed interest in the “fourth creatures.” Note that in the eight paragraphs mentioning fourth creatures, the term is twice put in quotes, along with being preceded once by “so-called.”
The Bible mentions fourth creatures, especially in Revelation. A review of this topic is included below.
Additionally, some related teachings about midway creatures, the Princes’s staff, Adam and Eve, and some higher order beings are included at the end.
Fourth creature(s)
(25:1.3) The number of servitals is prodigious, and more are being created all the time. They appear in groups of one thousand on the third moment following the assembly of the Master Spirits and the Supreme Power Directors at their joint area in the far northerly sector of Paradise. Every fourth servital is more physical in type than the others; that is, out of each thousand, seven hundred and fifty are apparently true to spirit type, but two hundred and fifty are semiphysical in nature. These fourth creatures are somewhat on the order of material beings (material in the Havona sense), resembling the physical power directors more than the Master Spirits.
(25:2.5) In each superuniverse the Universal Conciliators find themselves strangely and innately segregated into groups of four, associations in which they continue to serve. In each group, three are spirit personalities, and one, like the fourth creatures of the servitals, is a semimaterial being. This quartet constitutes a conciliating commission and is made up as follows:
(25:2.8) 3. The Divine Executioner. The conciliator qualified by inherent nature to make contact with the material beings of the realms and to execute the decisions of the commission. Divine executioners, being fourth creatures—quasi-material beings—are almost, but not quite, visible to the short-range vision of the mortal races.
(38:7.6) Cherubim and sanobim are by nature very near the morontia level of existence, and they prove to be most efficient in the borderland work of the physical, morontial, and spiritual domains. These children of the local universe Mother Spirit are characterized by “fourth creatures” much as are the Havona Servitals and the conciliating commissions. Every fourth cherubim and every fourth sanobim are quasi-material, very definitely resembling the morontia level of existence.
(38:7.7) These angelic fourth creatures are of great assistance to the seraphim in the more literal phases of their universe and planetary activities. Such morontia cherubim also perform many indispensable borderline tasks on the morontia training worlds and are assigned to the service of the Morontia Companions in large numbers. They are to the morontia spheres about what the midway creatures are to the evolutionary planets. On the inhabited worlds these morontia cherubim frequently work in liaison with the midway creatures. Cherubim and midway creatures are distinctly separate orders of beings; they have dissimilar origins, but they disclose great similarity in nature and function.
(38:8.4) 3. Morontia Cherubim. These “fourth creatures” of the angelic orders always retain their quasi-material characteristics. They will continue on as cherubim and sanobim, together with a majority of their mid-phase brethren, pending the completed factualization of the Supreme Being.
(39:1.15) The fourth creature bestowal of the Creator Son was in the likeness of a teaching counselor of the supreme seraphim of Nebadon.
(44:0.17) There are certain types of beings who are capable of discerning the reality of the creatures of both the spirit and the material worlds. Belonging to this class are the so-called fourth creatures of the Havona Servitals and the fourth creatures of the conciliators. The angels of time and space are endowed with the ability to discern both spirit and material beings as also are the ascending mortals subsequent to deliverance from the life in the flesh. After attainment of the higher spirit levels the ascenders are able to recognize material, morontia, and spirit realities.
Biblical perspective
Here is a review from compellingtruth.org of the Biblical perspective:
The Four Living Creatures in Revelation—Who are they?
The four living creatures in Revelation are special among the angelic beings. They exist to praise God forever before His throne, and they hold “golden bowls full of incense, which are the prayers of the saints” (Revelation 5:6-14). This means that they hold the prayers of all believers throughout time, both the prayers of the past and those that will be prayed—a fragrant offering before God’s throne (Revelation 8:3-4). This eternal fragrance was first symbolized by the incense burning in the tabernacle (Exodus 25:6).
The four living creatures are described in Revelation 4:6-9; 5:6-14; 6:1-8; 14:3; 15:7 and 19:4. They are said to be “full of eyes in front and behind” and look to John like a lion, an ox, a man, and an eagle in flight. They each have six wings and are always saying “holy, holy, holy is the Lord God Almighty, who was and is and is to come.” These four living creatures closely resemble the four creatures described in Ezekiel 1:10 and Isaiah 6:2. It is not clear whether these passages are describing the same four living creatures, but it is very likely they are of the same exalted order of angels, whose main job is to worship God and speak His holiness (Revelation 19:4). In response to the worship of the four living creatures, the twenty-four elders cast their crowns before God’s throne in agreement (Revelation 4:10-11).
One of the most interesting aspects of the four living creatures is that they demonstrate that Jesus, the Lamb of God, is equal to God Himself. Their worship of the Lamb in Revelation 5:6-14 is clearly directed towards Jesus Christ (Revelation 5:5; 9-10), and they say “Worthy is the Lamb who was slain, to receive power and wealth and wisdom and might and honor and glory and blessing!” (Revelation 5:11-12) and “To him who sits on the throne and to the Lamb be blessing and honor and glory and might forever and ever!” (Revelation 5:13) and they fall down and worship the Lamb, along with “him who sits on the throne” —God, the Father. Scripture makes it clear that “the Lord is God; there is no other besides him” (Deuteronomy 4:35; 1 Kings 8:60). God spoke through Isaiah, saying, “I am the Lord, and there is no other, besides me there is no God” (Isaiah 45:5-6) and Jesus Christ also responded to the Pharisees’ question about His identity by saying “before Abraham was, I am” (John 8:58). Based on their subsequent attempt to stone Jesus, we know that His statement “I am” was taken to mean “I am God” and the Pharisees took it as blasphemy. But the words and worship of the four living creatures make it clear that Jesus was telling the truth.
Midwayers
(77:5.6) Adamson and Ratta had a family of sixty-seven children. They gave origin to a great line of the world’s leadership, but they did something more. It should be remembered that both of these beings were really superhuman. Every fourth child born to them was of a unique order. It was often invisible. Never in the world’s history had such a thing occurred. Ratta was greatly perturbed—even superstitious—but Adamson well knew of the existence of the primary midwayers, and he concluded that something similar was transpiring before his eyes. When the second strangely behaving offspring arrived, he decided to mate them, since one was male and the other female, and this is the origin of the secondary order of midwayers. Within one hundred years, before this phenomenon ceased, almost two thousand were brought into being.
Quasi-material, quasi-physical vs. semimaterial
(50:3.5) These assistants to the Planetary Prince seldom mate with the world races, but they do always mate among themselves. Two classes of beings result from these unions: the primary type of midway creatures and certain high types of material beings who remain attached to the prince’s staff after their parents have been removed from the planet at the time of the arrival of Adam and Eve. These children do not mate with the mortal races except in certain emergencies and then only by direction of the Planetary Prince. In such an event, their children—the grandchildren of the corporeal staff—are in status as of the superior races of their day and generation. All the offspring of these semimaterial assistants of the Planetary Prince are Adjuster indwelt.
(50:4.9) A Planetary Prince is not visible to mortal beings; it is a test of faith to believe the representations of the semimaterial beings of his staff. But these schools of culture and training are well adapted to the needs of each planet, and there soon develops a keen and laudatory rivalry among the races of men in their efforts to gain entrance to these various institutions of learning.
(51:2.2) Adams and Eves are semimaterial creatures and, as such, are not transportable by seraphim. They must undergo dematerialization on the system capital before they can be enseraphimed for transport to the world of assignment. The transport seraphim are able to effect such changes in the Material Sons and in other semimaterial beings as enable them to be enseraphimed and thus to be transported through space from one world or system to another. About three days of standard time are consumed in this transport preparation, and it requires the co-operation of a Life Carrier to restore such a dematerialized creature to normal existence upon arrival at the end of the seraphic-transport journey.
(25:3.11) 5. Conciliators to the Superuniverse Minor Sectors. From the problems of local universes the commissioners are advanced to the study of questions arising in the minor sectors of their superuniverse. The farther they ascend inward from the individual planets, the fewer are the material duties of the divine executioner; gradually he assumes a new role of mercy-justice interpreter, at the same time—being quasi-material—keeping the commission as a whole in sympathetic touch with the material aspects of its investigations.
(116:4.5) These Master Spirits are not only the supporters and augmenters of the sovereignty of Supremacy, but they are in turn affected by the creative purposes of the Supreme. Ordinarily, the collective creations of the Master Spirits are of the quasi-material order (power directors, etc.), while their individual creations are of the spiritual order (supernaphim, etc.). But when the Master Spirits collectively produced the Seven Circuit Spirits in response to the will and purpose of the Supreme Being, it is to be noted that the offspring of this creative act are spiritual, not material or quasi-material.
(29:1.1) The Seven Supreme Power Directors are the physical-energy regulators of the grand universe. Their creation by the Seven Master Spirits is the first recorded instance of the derivation of semimaterial progeny from true spirit ancestry. When the Seven Master Spirits create individually, they bring forth highly spiritual personalities on the angelic order; when they create collectively, they sometimes produce these high types of semimaterial beings. But even these quasi-physical beings would be invisible to the short-range vision of Urantia mortals.