  In this paper, we invoke a generalized uncertainty principle (GUP) in the
symmetry-reduced cosmological Hamiltonian for a universe driven by a
quintessence scalar field with potential. Our study focuses on semi-classical
regime. In particular, we derive the GUP-distorted Friedmann, Raychaudhuri, and
the Klein-Gordon equation. This is followed by a systematic analysis of the
qualitative dynamics for the choice of potential $V(\phi)= V_0 \sinh^{-n}{(\mu
\phi)}$. This involves constructing an autonomous dynamical system of equations
by choosing appropriate dynamical variables, followed by a qualitative study
using linear stability theory. Our analysis shows that incorporating GUP
significantly changes the existing fixed points compared to the limiting case
without quantum effects by switching off the GUP.
