God created the Soul of Adam, and everyone afterwards has had a soul as a result. Pre-existence of all souls, It is believed by Mormons. Origen favored pre-existence of souls. Creationism , whereby God creates a fresh soul for each body. Roman Catholics and most Reformed and Calvinist Churches favor creationism.
Reincarnation is the belief that an individual human soul passes through a succession of lives.
No conventional Christian Denomination believes in reincarnation, but Hindus, Buddhists and Jainists do. Some Western groups DO believe in reincarnation, but they limit it to human form, where Eastern religions feel that reincarnation could involve any living creature. This seems to favor Traducianism, but arguments for the other alternatives have sometimes been offered based on that same Scripture. The concept of Soul is so esoteric that there are some scholars who deny the very existence of it, partly because there has never been any concrete evidence that proves its existence. Of course, in that event, any discussion regarding the origin of the Soul becomes meaningless.