Montmorillonite clay was chemically modified by grafting of 3-mercaptopropyl trimethoxy silane on the clay surface, followed by sulfonation of the terminal thiol groups. The chemical structures and surface characteristics of the prepared catalysts were characterized by FTIR, XRD, TPD, and BET analysis. The catalytic pyrolysis of Jatropha curcas oil and waste cooking oil for the production of biofuels was stimulated using the prepared catalyst. The conversion of oils into biofuels was performed at 350 °C using different catalysts amounts (0.2–1%). The obtained biofuels were characterized using density, flash, pour, and cloud points, water, sulfur, and ash contents, in addition to kinematic viscosity, copper strip, and carbon residue. Furthermore, the obtained biofuels were fractionated at 250 °C to obtain the light hydrocarbon components, which were evaluated as biojet fuel. The physical and fuel properties of biodiesel-petroleum diesel blends (B10), and biojet-JET A-1 blends were following the ASTM and IP specifications. The most suitable catalyst ratio during the catalytic cracking process was monitored at 0.8%.