Amorphous chalcogenide thin films are widely studied due to their enhanced properties and extensive applications. Here, we have studied amorphous Ga-Sb-Se chalcogenide thin films prepared by magnetron co-sputtering, via laser ablation quadrupole ion trap time-of-flight mass spectrometry. Furthermore, the stoichiometry of the generated clusters was determined which gives information about individual species present in the plasma plume originating from the interaction of amorphous chalcogenides with high energy laser pulses. Seven different compositions of thin films (Ga content 7.6–31.7 at. %, Sb content 5.2–31.2 at. %, Se content 61.2–63.3 at. %) were studied and in each case about ~50 different clusters were identified in positive and ~20–30 clusters in negative ion mode. Assuming that polymers can influence the laser desorption (laser ablation) process, we have used parafilm as a material to reduce the destruction of the amorphous network structure and/or promote the laser ablation synthesis of heavier species from those of lower mass. In this case, many new and higher mass clusters were identified. The maximum number of (40) new clusters was detected for the Ga-Sb-Se thin film containing the highest amount of antimony (31.2 at. %). This approach opens new possibilities for laser desorption ionization/laser ablation study of other materials. Finally, for selected binary and ternary clusters, their structure was calculated by using density functional theory optimization procedure.