And it came to pass, when men began to multiply on the face of the earth, and daughters were born unto them,

2 That the sons of God saw the daughters of men that they were fair; and they took them wives of all which they chose.

3 And the Lord said, My spirit shall not always strive with man, for that he also is flesh: yet his days shall be an hundred and twenty years.

4 There were giants in the earth in those days; and also after that, when the sons of God came in unto the daughters of men, and they bare children to them, the same became mighty men which were of old, men of renown.

• Genesis 6

At first it may truly seem that it is not in accordance with the Catholic Faith to maintain that children can be begotten by devils, that is to say, by Incubi and Succubi: for God Himself, before sin came into the world, instituted human procreation, since He created woman from the rib of man to be a helpmeet unto man: And to them He said: Increase, and multiply, Genesis ii, 24. Likewise after sin had come into the world, it was said to Noe: Increase, and multiply, Genesis ix, 1. In the time of the new law also, Christ confirmed this union: Have ye not read, that he who made man from the beginning, Made them male and female? S. Matthew xix, 4. Therefore, men cannot be begotten in any other way than this.

[...] And again in Genesis vi the gloss makes two comments on the words: And the sons of God saw the daughters of men. First, that by the sons of God are meant the sons of Seth, and by the daughters of men, the daughters of Cain. Second, that Giants were created not by some incredibly act of men, but by certain devils, which are shameless towards women. For the Bible says, Giants were upon the earth. Moreover, even after the Flood the bodies not only of men, but also of women, were pre-eminently and incredibly beautiful.

• Malleus Maleficarum

In antiquity there was the idea of sexual intercourse between humans and supernatural beings that would lead to live issue. This is most prominent in certain apochryphal and Manichaean works like The Book of Giants, but traces of the tradition survive in the Book of Genesis, and even in the Middle Ages there were traditions of demons or devils begetting children with mortals.

What happened to their grandchildren, great-grandchildren, and further descendants is often less clearly mapped out; folklore and legend usually only goes down a generation or two. But you had that idea of human mating with angels and demons.

Which is what the designers of Dungeons & Dragons were largely drawing on. D&D from the first edition began developing a Christian-influenced-but-unique approach to the afterlife, including the various angels, demons, and other creatures that existed there.

So in 1980, you got Deities & Demigods, which introduced many pantheons for use in Dungeons & Dragons games, sketched out a cosmology in the planes of existence that mapped out the "Outer Planes" to the ninefold arrangement of alignments that Gygax had created (two axes - Good and Evil from Christian thought, Law and Chaos from Michael Moorcock's Elric series, to give Lawful Good, Chaotic Good, Neutral Evil, Lawful Neutral, True Neutral, et. al) The book also introduced several classical demigods, and in the section of the Cthulhu Mythos, even mentioned the Spawn of Yog-Sothoth (from "The Dunwich Horror.")

The cambion, as an offspring of a demon and mortal woman, was introduced in the Monster Manual II (1983); the older mythological sense of "cambion" was closer to what we think of as "changeling" today, that is an incubus and succubus would have a child and substitute it for a human infant, but Gary Gygax used it to mean:

When a human female mates with a demon, the offspring is always a cambion male. The general characteristics and abilities of a cambion depend upon its parentage.

In later editions the cambion would become the "half-fiend," and the equivalent children of angels/celestial beings would be "half-celestials." Jeff Grubb expanded on the cosmology in Manual of the Planes (1987), and in 1994 all of that previous material was taken, revised, and expanded into the Planescape setting, which introduced Tieflings (descendants of half-fiends/cambions) and Aasimar (descendants of half-celestials).

So...there's a definite thread of mythological basis for them, but it would not be accurate to say that they were directly inspired by, say, the great-grandchildren of the Nephilim or something. It's really just a setting-specific example of extrapolating from existing mythological material.