  Numerous few-electron atomic systems are considered which can be used
effectively for observing a potential variation of the fine-structure constant
$\alpha$ and the electron-proton mass ratio $m_e/m_p$. We examine optical
magnetic dipole transitions between hyperfine-structure components in heavy
highly charged H-like and Li-like ions with observably high sensitivity to a
variation of $\alpha$ and $m_e/m_p$. The experimental spectra of the proposed
systems consist of a strong single line, which simplifies significantly the
data analysis and shortens the necessary measurement time. Furthermore, we
propose systems for an experimental test of the variation of quark masses and
discuss the expected level of accuracy in assessing its limitations. Finally,
we establish which constraints on the variation of these fundamental constants
could be provided by measurements with a hyperfine-structure highly-charged-ion
clock and some reference clock, showing that a significant improvement of the
current limitations can be reached.
