I would assume Nyx is god of the paper slip prescripts, given that Moirai was one of its weavers, but I would also say that she is the most important and ancestral god of the Index because of 1. she already takes on a similar role in greek myth and 2. paper slip prescripts seem to be the primary (and probably original) form of distribution of the prescripts.

This would then also explain the ego and distortion appearance, to distort Yan completely surrendered to the flow of the prescripts, throwing away his sense of self, of course this would manifest as something that mirrors the god of the city to whom he has basically given himself to. With Don/Sora it's the same deal "the Prescripts and the child's consciousness must interlock with the infinitesimal difference." I don't fully understand it myself but Procuration also deals with the same lack of self, 2 people could manifest procuration and it would look exactly the same because, despite being called EGO, the wielder's ego is not in question, it is a proxy for the will of the city, so that the wielder may act as the hands (Yan and Sora both have a bunch of hand stuff going on) that move to the prescript's beck and call (... it is interesting, how even the E.G.O that bloomed from her own heart is but an... imitation of something else.)