We analyze the behavior of several renormalization group functions at infrared fixed points for $SU(N)$ gauge theories with fermions in the fundamental and two-indexed representations. This includes the beta function of the gauge coupling, the anomalous dimension of the gauge parameter and the anomalous dimension of the mass. The scheme in which the analysis is performed is the minimal momentum subtraction scheme through third loop order. Due to the fact that scheme dependence is inevitable once the perturbation theory is truncated we compare to previous identical studies done in the minimal subtraction scheme and the modified regularization invariant scheme. We find only mild to moderate scheme dependence.