Quantum-dot cellular automata offer an intriguing paradigm in communication and computation as a potential replacement for CMOS technology. The fast-working speed, extremely low energy dissipation, and ultrahigh packing density make QCA incredibly appealing. This work proposes a 3-bit parity module using a layered T logic reduction methodology. The Costα, total, and average energies for the proposed LT modules are calculated and analyzed with the existing designs. It is stated that the suggested 3-bit even and odd parity generator layouts excel in reducing the power dissipation and cost. The bistable approximation and coherence vector simulation engines of QCADesigner 2.0.3 and QCA Designer E 2.2 with gallium arsenide heterostructure parameters are utilized in layout generation and energy estimation.