Potatoes from Galicia (northwestern Spain) are subjected to a Protected Geographic Indication (PGI) according to European legislation. Ten trace elements (Li, Na, K, Rb, Ca, Fe, Mg, Mn, Cu, and Zn) have been determined by atomic spectrometry in two sets of potato samples: Geo-Origin.set and Variety.set. The first data set is composed of samples of the only variety authorized by PGI (Kennebec) with two geographical origins: Galician and non-Galician. The second set corresponds to samples from different varieties but with only Galician geographical origin. Chemometric pattern recognition techniques have been applied to the study of potato geographical and varietal origins in relation to their capability for translocating metals from soil to tuber. Also, authentication models for classifying potato samples with Galician PGI based on metal fingerprints have been developed. The results obtained showed that samples of the same variety, Kennebec, have different metal fingerprints when they have been produced in different geographic locations. Also, diverse potato varieties cultivated on equal geographic Galician origin presented different metal profiles as well. Therefore, it can be concluded that classification studies on the differentiation of geographical origin of foods should take into account information of production area together with varietal data. Otherwise, classification obtained on the basis of the geographical origin could be due to the different variety or vice versa. Finally, two models were constructed for Kennebec Galician samples against Kennebec from other origins as well as against other varieties cultivated in Galicia (Liseta and Baraka). Both models achieved adequate classification rates (93-100%), good sensitivities, and total specificities (100%), allowing the fraud detection in the PGI label.