  This paper investigates static wormhole solutions through Noether symmetry
approach in the context of energy-momentum squared gravity. This newly
developed proposal resolves the singularity of big-bang and yields feasible
cosmological results in the early times. We consider the particular model of
this theory to establish symmetry generators and corresponding conserved
quantities. For constant and variable red-shift functions, we examine the
presence of viable traversable wormhole solutions for both dust as well as
non-dust matter distributions and analyze the stable state of these solutions.
We investigate the graphical interpretation of null and weak energy bounds for
normal and effective energy-momentum tensors to examine the presence of
physically viable wormhole geometry. It is found that realistic traversable and
stable wormhole solutions are obtained for a particular model of this gravity.
