The Advanced Encryption Standard (AES) is widely used and well-studied for its efficiency and strong security. This paper presents quantum circuit designs for the AES S-box by introducing the composite field ( F((2^4)^2) ) to replace the traditional field ( F(2^8) ), enabling the inversion to be decomposed into operations over ( F(2^4) ). This work reduces the quantum resource overhead required for implementing the S-box by decreasing the number of (CNOT) gates in the matrix multiplication, lowering the depth of (T) gates in both the inversion circuit and the multiplication circuit. Besides, the widths for the S-box quantum circuits are also optimized during the inversion circuit and multiplication circuit. With a linear key schedule, the resulting AES-128 quantum circuit reduce the product of the circuit width and (T) depth to 102800, which is the lowest known to date.