Magnetosheath reconnection due to the interaction of an interplanetary directional discontinuity with the bow shock and Earth's magnetosphere under an initially northward interplanetary magnetic field (IMF) has been investigated in previous simulations (e.g., Guo et al., 2018, https://doi.org/10.1029/2018ja025679). Under an initially southward IMF, the magnetosheath reconnection could interact with reconnection at the magnetopause. In this study, using three‐dimensional (3D) global‐scale hybrid simulations, we present cases with incoming tangential discontinuities (TDs) in an initially southward IMF, which possess various magnetic field rotation angles (ΔΦ) and half‐width (w), to study the effects of pre‐existing magnetopause reconnection on the formation of magnetosheath flux ropes, as well as the subsequent interaction between the magnetopause reconnection and magnetosheath reconnection, with downstreams of both Quasi‐perpendicular (Q‐⊥) and Quasi‐parallel (Q‐||) shock examined. The initial IMF is assumed to be oblique, with a finite Bx and Bz, similar to that in Guo et al. (2018), https://doi.org/10.1029/2018ja025679 but with a southward Bz < 0. Compared with the cases with an initially northward IMF, magnetopause reconnection weakens the compression processes of the TD and leads to less frequent reconnection in the magnetosheath. The existence and the structure of magnetosheath reconnection are found to strongly depend on the parameters w and ΔΦ of the TD. When interacting with the magnetopause reconnection, the magnetosheath flux ropes can re‐reconnect with the geomagnetic dipole field lines, forming new structures of magnetopause flux ropes. The resulting evolution of flux rope configuration is illustrated.