A novel handwritten English alphabet recognition technique based on persistent homology for the first time in literature, to the best of our knowledge, is proposed in this paper. Given a set of 26 English alphabet images as standard and an input handwritten alphabet image, the point cloud of each image is subjected to persistent homology techniques to generate simplicial complexes at different radii. The persistence of topological features, like hole, across several radii is represented in the form of 3D Barcode diagram, a theoretical concept newly proposed in this paper. The 3D Barcode diagrams of a handwritten alphabet and a standard alphabet are compared by generating a similarity score that determines the output set of standard alphabets. The result is refined using topological equivalence based on the concept of isomorphism of homology groups. Extensive experimentation has produced encouraging results with an accuracy of 81%.