I have read in some places that the Trinity doctrine as presented by the WT publications for dissection is not really the Trinity doctrine but actually is an apostate doctrine from the original Trinity doctrine.
Maybe you are thinking of modalism, which is what the WTS sometimes mistakes the Trinity doctrine to be. This is the claim that the Father, Son, and Holy Spirit are all God, but as one person in different functions or roles. There is some incipient modalism in Ignatius and probably elsewhere in early Christianity (e.g. the Pauline equivalence between the Holy Spirit and a pneumatic Christ), but explicit modalism was rejected by orthodoxy in the second century. BTW, the Trinity doctrine favored by Tertullian and some other second-century apologists involved an economical tri-unity and thus lacked the concept of the persons being co-eternal and co-equal, as it is formulated in the Nicene creed and in apologists in the third century onward....