The heavy fermion compound Ce3Pd20Si6 is one of the rare examples of a cubic system with a readily accessible quantum critical point. Ce atoms at the two different sites 4a and 8c of the crystal structure have recently been shown to have different crystal field ground states (Γ7 and Γ8, respectively) and are assumed to be responsible for the two different low-temperature phase transitions at T(L) and T(U), which have been tentatively attributed to antiferromagnetic and antiferroquadrupolar order, respectively. Here we present electrical resistivity measurements in a wide temperature range (50 mK-300 K) on two new representatives of the La substitution series Ce(3 - x)La(x)Pd20Si6, x=1/3 and 2/3. Put in the context of previously published data our results indicate that La preferentially occupies the 4a site and that Ce ions at the 8c site have a sizably larger Kondo temperature. Low-temperature resistivity measurements in applied magnetic fields suggest that (disorder smeared) quantum critical points exist in the x=1/3 and 2/3 samples at fields below 1 T.