  In this paper we investigate the behaviour of massless fermions in the black
string spacetime by computing the eigenvalues and eigenfunctions of the Weyl
equations. These solutions allowed us to study the behaviour of such massless
fermions in terms of the cosmological constant, the black string's mass and the
radial distance of the particle from the black string. The solutions, written
in terms of Parabolic Cylinder functions and Laguerre polynomials, were
obtained for a particle far from the black string and around the horizon event.
For the particle around the event horizon, for all configuration of parameters,
the energy eigenvalues are complex-valued, indicating QNM similarly to the case
of spherical black holes. For the particle far from the black string, the
energies derived from the Weyl equation set up conditions on the parameters in
order to keep the energy as a real valued parameter.
