A pair of dual-purpose superconducting quadrupole magnets and a superconducting detector solenoid were fabricated and installed in Beijing Electron-Positron Collider Upgrade (BEPCII). The magnets are symmetrically inserted into the BESIII detector with respect to the interaction point. They are identical, iron-free, non-collared, multi-layered and active shielded superconducting magnets for the micro-beta focusing at the interaction region of the collider rings. Each quadrupole magnet is composed of seven coils at different operating currents wound layer by layer on a common cylindrical support. The magnet has an overall effective length of 0.96 m and provides a good field aperture of 65 mm in diameter. They are cooled by supercritical helium in order to eliminate the flow instabilities in constrained cooling channels. The BESIII superconducting solenoid magnet was designed to provide an axial magnetic field of about 1.0 T over the tracking volume and to meet the requirement of particle momentum resolution to particle detectors. A single layer of coil, in-direct cooling by forced two-phase helium, high purity aluminum based stabilizer and NbTi/Cu superconductor is adopted for the solenoid. The solenoid is 3.4 m in diameter and 3.89 m in length. This paper presents the design of the superconducting magnets in the BEPCII as well as their cryomodules. The cooling system for the magnets is also discussed.