Which one is correct?
Either in the first or second version
Either in the first or second versions
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To my mind, the first version is correct.
You are talking about one version, right? Even if you don't know which version, you know it's exactly one, so it's singular.
Here is an example where you could use a plural:
In both the first, and also either the second or third, but not fourth or fifth versions.
Here I used the plural because I know it's exactly two versions.