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We present an asymmetric $q$-Painlev\'e equation. We will derive this using$q$-orthogonal polynomials with respect to generalized Freud weights: theirrecurrence coefficients will obey this $q$-Painlev\'e equation (up to a simpletransformation). We will show a stable method of computing a special solutionwhich gives the recurrence coefficients. We establish a connection with$\alpha-q-P_V$.

$q$-Discrete Painlev\'e equations for recurrence coefficients of modified $q$-Freud orthogonal polynomials