We consider the problem of constructing a conjugate (1/q, q)-harmonic homogeneous polynomial \(V_k\) of degree k to a given (1/q, q)-harmonic homogeneous polynomial \(U_k\) of degree k. The conjugated harmonic polynomials \(V_k\) and \(U_k\) are associated to the (1/q, q)-monogenic polynomial \(F = U_k + \overline{e}_0V_k. \) We investigate conjugate (1/q, q)-harmonic homogeneous polynomials in the setting of q-Clifford analysis. Starting from a given (1/q, q)-harmonic polynomial \(U_k\) of degree k, we construct its conjugate counterpart \(V_k\) , such that the Clifford-valued polynomial \(F = U_k + e_0 V_k\) is (1/q, q)-monogenic, i.e., a null solution of a generalized q-Dirac operator. Our construction relies on a combination of Jackson-type integration, Fischer decomposition, and the resolution of a q-Poisson equation. We further establish existence and uniqueness results, and provide explicit representations for conjugate pairs, particularly when \(U_k\) is real-valued.