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We argue that in order to study the magneto-transport in a relativistic Weylfluid, it is needed to take into account the associated quantum corrections, namely theside-jump effect, at least to second order. To this end, we impose Lorentz invariance toa system of free Weyl fermions in the presence of the magneticfield and find the secondorder correction to the energy dispersion. By developing a scheme to compute the integralsin the phase space, we show that the mentioned correction hasnon-trivial effects on thethermodynamics of the system. Specifically, we compute the expression of the negativemagnetoresistivity in the system from the enthalpy densityin equilibrium. Then in analogywith Weyl semimetal, in the framework of the chiral kinetic theory and under the relaxationtime approximation, we explicitly compute the magneto-conductivities, at low temperaturelimit (T