Conduction does not only occur by doping. You can also induce metal insulator transition by pressure be it chemical or external. 

Fe2+ or Fe 3+ ions  behave in a crystal lattice as means to promote Verwey's Hopping Transition Mechanism.  

I f the Ga1-xScxFeO3.about which you are refering belongs to the SPINEL fAMILY 

THE PROCESS IS STILL TO BE UNDERSTOOD . sOMANY WORKERS ARE WORKING IN THIS LINE and LITERATURE IS AVAILABLE 

Off stoichiometry (either cation or anion) could also be the reason. Creates vacancies.

My opinion, most of the metal oxide-based perovskite systems exhibit a little oxygen vacancy, as a result of that the charge of the compound is not fully neutral. To achieve a charge neutrality between the cations and anions, one of the cations has to change its oxidation state and thereby metal ions will be in different oxidation state (eg, Fe in 2+ as well as 3+ states).....

I suggest you to perform a wide and deep study of Impedance Spectroscopy on your materials because "conductivity" can be the result of a set of electrochemical processes. Please take into account the bulk and grain boundary contributions from the oxide ions (and their vacancies) and do not disregard the electronic contribution since, in such a material, the presence of both species for Fe ( Fe(II) amd Fe(III) ) could be always taken as a fact (the same happens with Ce oxides...). Nyquist diagrams should give you answers and studies of activation energies for the processes can be a good characterization for the electrochemical behavior of these oxides.  In addition, I suggest, if you can access to this technology, to try Mossbauer Spectroscopy to understand better the crystallographic characteristics of Fe in these samples. Greets from Mendoza, Argentine. 

Conduction arises due to many factors including the presence of same ions in multi valence state (for example, Fe2+ and Fe3+), oxygen or cation vacancies, microstructural contributions from grains, grain-boundaries, interfaces, defects, etc.as partly mentioned in the earlier comments. It is not clear how your really arrive at a conclusion that there is no perceptible change in the Fe2+ content. Is it based on an experimental  support ? or you simply presume it because the iron content in your oxide perovskites kept unaltered throughout the substitutions. In general, non-uniform temperature gradients and atmospheres during firing would create off stoichiometric conditions resulting in generating all the conduction sources mentioned above. I agree with the comment of Gustavo that impedance spectroscopy, chemical analysis, XPS study and/or Mossbauer spectroscopy would throw more light in understanding the source of conductivity in these compounds.

I agree with above specially with Dr. Rao, But what surprises me, perhaps unnoticed is this part of your question:  "why do we find conductivity in these samples?": Means (what i understand) sample is conducting or metallic even at Room Temperature.  if it is true, then go for low temperature conductivity, conductivity should decrease.

I found your question lack clarity. Still want to say pure H-atom can be insulator or conductor but in different condition. Thus, Definition of insulator and conductor is complex and condition based not  impurity based.

still want to say any Oxide materials, must has Oxygen vacancy, thus ferrite has Fe+2 and Fe+3 state,as explained by others.

Thank you all.

My sample is not a spinel.