  In this paper, we have presented the Noether symmetries of flat FRW spacetime
in the context of a new action in Teleparallel Gravity which we construct it
based on $f(R)$ version. This modified action contains a coupling between
scalar field potential and magnetism. Also, we introduce an innovative approach
(B.N.S. Approach) for exact solutions which carry more conserved currents than
Noether approach. By data analysis of the exact solutions, obtained from
Noether approach, late time acceleration and phase crossing are realized, and
some deep connections with observational data such as the age of the universe,
the present amounts of the scale factor as well as the state and deceleration
parameters are observed. In B.N.S. approach, we have considered dark energy
dominated era.
