  Three-dimensional doped Dirac insulators foster simply connected (in both
topological and trivial regimes) and annular (deep inside the topological
regime) Fermi surfaces (FSs) in the normal state, and allow on-site repulsions
among fermions with opposite spin ($U_1$) and parity ($U_2$) eigenvalues. From
an unbiased leading-order (one-loop) renormalization group analysis, controlled
by a suitable $\epsilon$ expansion, we show that this system develops strong
propensity toward the nucleation of scalar $s$-wave and odd-parity pseudoscalar
$p$-wave pairings, favored by repulsive $U_1$ and $U_2$ interactions,
respectively, irrespective of the underlying FS topology. Our results can be
pertinent for the observed superconductivity in various doped narrow gap
semiconductors, and the theoretical foundation can readily be applied to
investigate similar phenomenon in various doped topological materials.
