"It is not him coming in, but me."
Translation:Nem ő jön be, hanem én.
"Bejön" is a word. A verb with a preverb at the front of it. "In"+"comes". In negative statements like this, if the emphasis is not on the verb, it gets split like it did here. Here the emphasis is on the subject. The subject is being negated: "Nem ő". Keep searching and reading the discussions on splitting verbs, there are lots and lots.
One way I've seen it explained is that something you emphasise/focus wants to go right in front of the verb -- here, you are contrasting "not him" with "me", and so this "not him" gets emphasised by going in front of the verb.
And it wants to be right in front of the verb so strongly that even preverbs such as be- have to make way so that the nem ő can be right in front of the (base) verb (jön in this case).
It goes even further. It's somewhat informal, but if a question has a non-empty focus, you can answer with just repeating the focus (meaning yes.)
Az ajtóhoz ment?
Az ajtóhoz. (Igen.)
Now, if the preverb doesn't separate in the question, you can do the same, but repeating the preverb:
So sometimes it's worth thinking of preverbs as separate words, imo.