What parameters should be set for an unholy Trinity to be worshipped as one bein

Just say it is so. They are all parts and facets of the same end point. If you have to justify it, make that the focus.

 

Catholics see no difficulty in squaring that circle.
Christianity is not something I know a lot about theologically so I can't go in to the dogma and doctrine of why that might be the case.
And who said a religion had to be logical anyway...

 

It sounds like the son would be what the greeks called a demigod, or half-god. Since the god being an evil thing that would wipe out nearly all life in the world with a massive global cataclysm, then after the few survivors have repopulated would then burn whole cities and command his followers to genocide (or some such general wickedness) if they could actually embody themselves physically in the world. So in order for the world to be a place that mortals can survive long enough for there to be a story they are barred from actually just getting down with their evil self. So they'd create a demigod son to do evil on their behalf.

Of course it would be ironic if the half god of such an evil deity turned out to be a nice guy, but I'm sure even those who claimed to follow the nice-guy demigod would still worship the evil deity too because sometimes you have to have an excuse to torture and burn people, and do genocide cuz reasons. But I digress...

 

In Greek mythology, Zeus didn't stop impregnating mortal women and nymphs just because he already had a child or a few out there. In Christianity, Mary isn't divine (except when she is). Why can't multiple aspects of God be running around on Earth in mortal form? Why should the mother of a divine child have to be divine herself? Existing traditions say otherwise.

 

I think the only way to make it work is to make the mom not-human. Perhaps she’s a physical reflection or emanation of Zoth. Sort of an avatar but mirrored gender-wise due to being grounded in the physical world. Then maybe she does a virgin birth thing to give birth to the direct physical incarnation of Zoth. So Zoth emanates as the woman who asexually produces the evil messiah guy.
So Zoth is the demon in god form, the woman is the demon in demigod form and the child is the demon in human form. Sort of like how air, water and ice are all H2O in different physical states.

If you try looking at Hinduism, there’s a lot of examples of reverse-gender avatars, and gods interacting with their avatars, divine being reproducing asexually, all kinds of junk like that.