A spectroscopic study of a shallow donor and its bound exciton (BE) in narrow GaAsIAlGaAs quantum wells (QWs) has been performed. The electronic structure has been investigated by means of selective photoluminescence (SPL) and PL excitation (PLB) spectroscopy; The excited states of the confined Si donor have been monitored via two electron transitions (TETs) of the confined donor BE, observed in SPL and PLE spectra. The energy position of the observed TET satellite yields a value on the 1s -2s energy separation of 10.6 meV for a donor in the center of a 100 A wide QW, which is in excellent agreement with recent theoretical predictions. Similar measurements have also been performed in a magnetic field. While the donor BE shifts towards higher energy with increasing field, with a diamagnetic shift similar to the free exciton, the TET satellite is found to shift considerably towards lower energies, i.e. the 1s -2s energy separation increases with increasing magnetic field. To the best of our knowledge, this SPL study constitutes the first investigation of the magnetic field dependence of s-like excited states of the confined donor, since only transitions between the ground state and p-like excited donor states, observed in optical absorption, have been experimentally studied up to now.