We have studied theoretically the type-II GaAsSb capped InAs quantum dots for two structures differing in the composition of the capping layer, being either (i) constant or (ii) with Sb accumulation above the apex of the dot. We have found that the hole states are segmented and resemble the states in the quantum dot molecules. The two-hole states form singlet and triplet with the splitting energy of 4{\mu}eV / 325{\mu}eV for the case (i) / (ii). We have also tested the possibility to tune the splitting by vertically applied magnetic field. As the predicted tunability range was limited, we propose an approach for its enhancement.
