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The question is here asked whether God is in any genus. By "genus" is meant the "logical genus." "Logical genus" is that overarching category that contains many species. The highest genera are called the "categories" by Aristotle.
Thus, this question is asking whether God's essence (declared to be his existence in a.4) is composed of genus and species (i.e., logical composition)
In this article, St. Thomas gives three proofs.
First, from the nature of a genus. A genus is related to a species as perfectible and perfected. We may think of the relationship as analogous to the relationship of nature/suppositum, form/matter, and existence/essence that we have discussed beforehand. Now, the same argument can be leveled against God being in a genus as we have leveled against God having matter, i.e., it would add some potency to God.
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