  Large-scale coherent magnetic fields observed in the nearby galaxies are
thought to originate by a mean-field dynamo. This is governed via the turbulent
electromotive force (EMF, $\overline{\mathcal{E}} $) generated by the helical
turbulence driven by supernova (SN) explosions in the differentially rotating
interstellar medium (ISM). In this paper we aim to investigate the possibility
of dynamo action by the virtue of buoyancy due to a cosmic ray (CR) component
injected through the SN explosions. We do this by analysing the
magnetohydrodynamic simulations of local shearing box of ISM, in which the
turbulence is driven via random SN explosions and the energy of the explosion
is distributed in the CR and/or thermal energy components. We use the magnetic
field aligned diffusion prescription for the propagation of CR. We compare the
evolution of magnetic fields in the models with the CR component to our
previous models that did not involve the CR. We demonstrate that the inclusion
of CR component enhances the growth of dynamo slightly. We further compute the
underlying dynamo coefficients using the test-fields method, and argue that the
entire evolution of the large scale mean magnetic field can be reproduced with
an $\alpha-\Omega$ dynamo model. We also show that the inclusion of CR
component leads to an unbalanced turbulent pumping between magnetic field
components and additional dynamo action by the R\"adler effect.
