  In this paper, we study the relativistic and nonrelativistic Landau levels
for Dirac fermions in the cosmic string spacetime in the context of rainbow
gravity in $(3+1)$-dimensions, where we work with the curved Dirac equation
with minimal coupling in cylindrical coordinates. Using the tetrads formalism
of General Relativity, we obtain a second-order differential equation. Solving
this differential equation, we obtain a generalized Laguerre equation as well
as the relativistic Landau levels for the fermion and antifermion, where such
energy levels are quantized in terms of the quantum numbers $n$, $m_j$ and
$m_s$, and explicitly depends on the rainbow functions $f(\varepsilon)$ and
$g(\varepsilon)$, charge parameter $\sigma$, cyclotron frequency $\omega_c$,
curvature parameter $\alpha$, and on the square rest energy $m^2_0$ and square
$z$-momentum $k^2_z$, respectively. Posteriorly, we study the nonrelativistic
limit of the system, where we obtain the nonrelativistic Landau levels. In both
cases (relativistic and nonrelativistic), we graphically analyze the behavior
of Landau levels for the three rainbow gravity scenarios as a function of the
magnetic field $B$ and of the curvature parameter $\alpha$. In addition, we
also compared our problem with other works, where we verified that our results
generalize several particular cases in the literature.
