  We modify the symmetric-teleparallel dark energy through the addition of a
further Yukawa-like term, in which the non-metricity scalar, $Q$, is
non-minimally coupled to a scalar field Lagrangian where the phion acts as
quintessence, describing dark energy. We investigate regions of stability and
find late-time attractors. To do so, we conduct a stability analysis for
different types of physical potentials describing dark energy, namely the
power-law, inverse power-law, and exponential potentials. Within these choices,
we furthermore single out particular limiting cases, such as the constant,
linear and inverse potentials. For all the considered scenarios, regions of
stability are calculated in terms of the signs of the coupling constant and the
exponent, revealing a clear degeneracy among coefficients necessary to ensure
stability. We find that a generic power-law potential with $\alpha > 0$ is not
suitable as a non-minimal quintessence potential and we put severe limits on
the use of inverse potential, as well. In addition, the equations of state of
each potential have been also computed. We find the constant potential seems to
be favored than other treatments, since the critical point appears independent
of the non-minimal coupling.
