"The most important and most problematic of the characterizations of Thomism concerns the third point immediately mentioned above: the idea that God and creatures might be understood in Thomism as species of a common genus by appeal to either the concept of being or of causality. Due to his rhetorical style, it is difficult to tell how aware Barth is of the depth of miscomprehension of classical and medieval thought that this characterization represents. Spencer, at any rate, repeats the charge as if it were unproblematic. Yet leaving aside for the moment any question of  God, according to both Aristotle and Aquinas, as well as other influential medievals such as Scotus and Suarez, being and causality, even in  realities we experience immediately, are never themselves confined to realization within a single genus. To think that they could be is in fact to have fundamentally misunderstood one of the most basic structures of classical metaphysics, such that a charge like this one renders a serious dialogue between Thomists and Barthians nearly impossible. For contrary to this account . . . of the 'analogia entis,' it is precisely against such an idea (of generic predication) that Aristotle focused upon the metaphysical truth that notions such as being, oneness, goodness, and truth (all of which he names explicitly in this respect) are not in any one genus of being, but said analogously of the diverse genera of being, by proportionality. Being is ascribed analogically to substances, natures, qualities, quantities, relations, operations, and so on because it is not reducible to any one of the categorical modes of being. The analogical and transcendental structure of being by its very nature implies the impossibility of the idea that being could be signified in a generic fashion. Furthermore, because there are four causes for Aristotle and Aquinas (formal, material, final, and efficient), causality itself is understood also without reference to one genus, and is understood only in a diversified fashion.
"What I have mentioned here refers, of course, only to  created beings. When it comes to the question of signifying  God analogically, even greater problems emerge with the Barthian portrait of St. Thomas. For, in fact, as Thomist historians commonly emphasize, Aquinas is quite insistent that even the transcendental notion of being (which is non-generic) only signifies the 'common being' (ens commune) that is found in all creatures. It does not in itself signify God in any way, insofar as God is not a member of ens commune. Consequently, God is not an object within the science of being as such (such that he could be considered as a 'being' alongside ontic creatures), but can only be approached tangentially by the human mind as the transcendent cause of all that exists. This is why we must say, for Aquinas, that not only is God not in a genus of being whatsoever (such as substance, or quantity, or operation, or relation), but he is not even a member of the set of all beings as such. He utterly transcends all that exists, all that is common to being, all that has being (signified variously as ens commune, or esse commune)."
Thomas Joseph White, O.P., "How Barth got Aquinas wrong: a reply to Archie J. Spencer on causality and Christocentrism," Nova et vetera: the English edition of the international theological journal 7, no. 1 (Winter 2009): 252-254 (241-269). "Not only is God not a member of any genus of being. In addition, he can only be understood as the transcendent cause of the subject of metaphysics (ens commune), that is to say, as the cause of everything that depends for its existence on another, and who is himself uncaused" (not causa sui!) (243n3).