  We consider a cosmological scenario endowed with an interaction between the
universe's dark components $-$ dark matter and dark energy. Specifically, we
assume the dark matter component to be a pressureless fluid, while the dark
energy component is a quintessence scalar field with Lagrangian function
modified by the quadratic Generalized Uncertainty Principle. The latter
modification introduces new higher-order terms of fourth-derivative due to
quantum corrections in the scalar field's equation of motion. We then
investigate asymptotic dynamics and general behaviour of solutions of the field
equations for some interacting models of special interests in the literature.
At the background level, the present interacting model exhibits the
matter-dominated and de Sitter solutions which are absent in the corresponding
quintessence model. Furthermore, to boost background analysis, we study
cosmological linear perturbations in the Newtonian gauge where we show how
perturbations are modified by quantum corrections terms from the quadratic
Generalized Uncertainty Principle. Depending on the coupling parameters, scalar
perturbations show a wide range of behavior.
