  We study a model where the Standard Model is augmented with three sterile
neutrinos. By adopting a particular parameterization of a $(6\times6)$ unitary
matrix - in this context, light neutrino masses being generated via a type-I
seesaw mechanism - we analytically derive the masses of the sterile states
using an exact seesaw relation. The masses of the sterile states are derived in
terms of the lightest mass of active neutrinos and active-active and
active-sterile mixing angles and phases; they can be all light, all heavy, or a
mixture of light and heavy compared to the active states. This can be
attributed to the interplay of the $CP$ violating (CPV) phases of the mixing
matrix. As both active and sterile states can mediate the neutrinoless double
beta decay ($0\nu\beta\beta$) process, their contributions to the effective
mass of the electron neutrino, $\lvert m_{ee}\lvert$, become a function of the
mass of the lightest active state and active-active and active-sterile mixing
angles and phases. We explore the parameter space of $\lvert m_{ee}\lvert$,
keeping in mind, the present and future sensitivity of $0\nu\beta\beta$ decay
searches. By making use of constraints from charged lepton flavor violating
(cLFV) processes and non-unitarity, we explore the role of additional CPV
phases and active-sterile mixing angle values. The numerical values thus
obtained for $\lvert m_{ee}\rvert$ can vary from as low as
$\mathcal{O}(10^{-4})$ to saturating the present experimental limit. We check
the reliability of our result by calculating the branching ratio of $\mu
\rightarrow e \gamma$, a prominent cLFV process, and non-unitarity in this
framework.
