The Hindus had a Trimurti, which was a triad of three of their multitude of gods, Brahma, Vishnu and Shiva. However it is most unlikely that this, or any other pagan beliefs, had any significant effect on the doctrine of the Trinity. The doctrine is not taught in the New Testament, but was the outcome of debates among Christian theologians about the nature of Christ, and was formulated in the fourth century AD. The question arose because God, of spirit nature, was Jesus’ father, and Mary, of human nature was his mother. Did that make Jesus of spirit nature or was he mortal like all other human beings? This question had been answered by Jesus’ himself in Luke 24:39 when he said, “A spirit does not have flesh and bones as you see me have”, and in Hebrews 2:14-18, which teaches very clearly that Jesus was of the same nature as all human beings.
Broughton and Southgate. The Trinity: true or false? Chapter 8.