We investigate a variant of the SSH model consisting of an SSH chain with an embedded Aharonov-Bohm quantum ring. The embedded ring gives rise to domain wall states whose energy levels are in the band gap. The dependence of some of the states on the ring's magnetic flux provides a mechanism to control the entanglement between the two SSH edge fermion modes. The concurrence between the edge modes depends periodically on the magnetic flux. In the deep topological zone, for appropriate values of the flux, the concurrence reaches the extreme values of 0 and 1, corresponding to vanishing entanglement and to maximum entanglement. Therefore, the QR-SSH system offers a tuning mechanism that can be used either as an entanglement modulator or as an entanglement switch.