ので in これが僕ので、それが君のだ。

What does ので in これが僕ので、それが君のだ mean exactly?
(Translation: This is mine, and that’s yours.)

I think in this case the 「で」 is the 〜て form of 「だ」.

The 〜て form is used to join two sentences happening at the same time in this case.