We employed dissipative particle dynamics simulations to explore the phase behavior of T-shaped ternary amphiphiles composed of rodlike cores connected by two incompatible end chains and side grafted segments. By fine-tuning the number of terminal and lateral beads, three phase diagrams for the model systems with different terminal chain lengths are constructed in terms of temperature and lateral chain length, which have some common features and mostly compare favorably with experimental studies with the exception a couple of new phases. It is worthwhile to highlight that the mixed cylindrical phase and the perforated layer phase, as the experimentally observed mesophases exclusive for facial amphiphilies, are found in simulations for the first time. Also, a novel gyroid structure is observed in series of T-shaped ternary amphiphiles for the first time. Furthermore, by evaluating the effective volume fraction of lateral chains, the phase sequence spanning from conventional smectic layer phase via perforated layer structures and polygonal cylindrical arrays to novel lamellar mesophase is established, which is not just qualitatively consistent with the related experimental findings but even the stability windows of some mesophases quantitatively correspond well to experimental results. The success of reproducing the in-plane ordering of rods in the lamellar phase as well as the generic phase diagram of such T-shaped ternary amphiphiles in great detail implies that our genetic model qualitatively captures many of the characteristics of the phase behavior of real T-shaped molecules and could serve as a satisfactory basis for further exploration of self-organization in other related soft matter systems.