  In this article we derive the exact dynamics of a two qubit (spin 1/2) system
interacting centrally with separate fermionic baths composed of qubits in
thermal state. Further, each spin of a bath is coupled to every other spin of
the same bath. The corresponding dynamical map is constructed. It is used to
analyse the non-Markovian nature of the two qubit central spin dynamics. We
further observe the evolution of quantum correlations like entanglement and
discord under the influence of the environmental interaction. Moreover, we
demonstrate the comparison between this exact two qubit dynamics and the
locally acting fermionic central spin model. This work is a stepping stone
towards the realization of non-Markovian heat engines and other quantum thermal
devices.
