  We calculate the first three Seeley-DeWitt coefficients for fluctuation of
the massless fields of an $\mathcal{N}=2$ Einstein-Maxwell supergravity theory
(EMSGT) distributed into different multiplets in $d=4$ space-time dimensions.
By utilizing the Seeley-DeWitt data in the quantum entropy function formalism,
we then obtain the logarithmic correction contribution of individual multiplets
to the entropy of extremal Kerr-Newman family of black holes. Our results allow
us to find the logarithmic entropy corrections for the extremal black holes in
a fully matter coupled $\mathcal{N}=2,d=4$ EMSGT, in a particular class of
$\mathcal{N}=1,d=4$ EMSGT as consistent decomposition of $\mathcal{N}=2$
multiplets ($\mathcal{N}=2 \to \mathcal{N}=1$) and in $\mathcal{N} \geq 3,d=4$
EMSGTs by decomposing them into $\mathcal{N}=2$ multiplets ($\mathcal{N} \geq 3
\to \mathcal{N}=2$). For completeness, we also obtain logarithmic entropy
correction results for the non-extremal Kerr-Newman black holes in the matter
coupled $\mathcal{N} \geq 1,d=4$ EMSGTs by employing the same Seeley-DeWitt
data into a different Euclidean gravity approach developed in arXiv:1205.0971.
