The phrase "according to another version" is correct and usable in written English.
It can be used when referencing a different interpretation or retelling of a story, event, or piece of information.
Example: "The tale of the hero varies greatly; according to another version, he was not alone in his quest."
Alternatives: "as per another account" or "in another telling".
According to another version, he embarked upon a raft made of snakes and disappeared beyond the eastern horizon.
(According to another version, the Graiae merely directed him to the Stygian Nymphs, who told him where to find the Gorgons and gave him the bag, sandals, and helmet; Hermes gave him the sword).
Later, when the truth became known, Jocasta committed suicide, and Oedipus (according to another version), after blinding himself, went into exile, accompanied by Antigone and Ismene, leaving his brother-in-law Creon as regent.
According to another version (recounted by Tacitus and almost certainly fiction) he reached the Greek islands, where the following year (69) the governor of Cythnos (modern Kíthnos) recognized him in the guise of a red-haired prophet and leader of the poor, had him arrested, and executed the sentence that had been passed by the Senate.
According to another version of internalism, if an agent judges that it is right for her to φ in circumstances C, then either she is motivated to φ, or she is irrational (Smith, 1994, 61; Korsgaard 1996).
According to another version of the story, Felix travelled from Gaul and reached the hamlet of Babingley, via the River Babingley.
According to another formula, the "Elo Chess" version of Jeff Sagarin's ratings - which also does not account for margin of victory but is designed more sensibly than R.P.I. - Washington had just the 42nd-best performance among the 68 tournament teams, which would be more in line with a No. 11 seed.
He later travelled to Spain, where his gambling instincts won him almost £30,000 - on the lottery, according to one version of events; on a complicated accumulator bet on the horses, according to another.
According to another version what we'll call pluralism all concrete facts that aren't grounded in such facts concern proper parts of the world, say point-sized particles or point-sized regions.
Retribution, according to yet another version, was immediate and harsh: rebels were rounded up and lynched.
According to one version, he was to strap dynamite to his body; in another, he was to blow himself up in a rigged minibus.
