  We explore wormhole solutions in a non-minimal torsion-matter coupled gravity
by taking an explicit non-minimal coupling between the matter Lagrangian
density and an arbitrary function of torsion scalar. This coupling depicts the
transfer of energy and momentum between matter and torsion scalar terms. The
violation of null energy condition occurred through effective energy-momentum
tensor incorporating the torsion-matter non-minimal coupling while normal
matter is responsible for supporting the respective wormhole geometries. We
consider energy density in the form of non-monotonically decreasing function
along with two types of models. First model is analogous to curvature-matter
coupling scenario, that is, torsion scalar with $T$-matter coupling while the
second one involves a quadratic torsion term. In both cases, we obtain wormhole
solutions satisfying null energy condition. Also, we find that the increasing
value of coupling constant minimizes or vanishes the violation of null energy
condition through matter.
