A 13 T Nb₃Sn common-coil accelerator-type magnet is being developed at the Paul Scherrer Institute (PSI). The magnet cross-section features an innovative design with asymmetric elements and effective stress-management. Thanks to the asymmetric design narrow pole racetrack coils are not required in proximity of the magnet apertures to improve the field quality. Its magnetic design achieves adequate margin with respect to the short-sample limit while utilizing two available cables. This choice accelerates the completion of the 0.8 m long demonstrator magnet, but limits the flexibility of the conductor grading and makes the magnet quench protection more challenging. In this contribution, the strategy to limit the hot-spot temperature and peak voltage to ground reached in the magnet conductor after a quench is discussed. The electro-magnetic and thermal transients occurring during a quench discharge are simulated with the STEAM-LEDET program. Quench detection based on differential-voltage monitoring is proposed, and the expected quench detection times are evaluated in the case of quenches occurring in different coil locations. Furthermore, the performances of various quench protection systems, including energy-extraction based either on a resistor or a varistor, a CLIQ (Coupling-Loss Induced Quench) system, or combinations of these are assessed. It is shown that while energy-extraction is a viable option to protect the magnet, acceptable performance can be achieved with CLIQ while achieving a significantly lower peak voltage to ground. The lowest hot-spot temperature is obtained by combining energy extraction and CLIQ.