The effects of metal-modified acidic co-supports on the hydrodesulfurization (HDS) activity and isomerization selectivity of highly refractory organosulfur compounds such as 4,6-dimethyldibenzothiophene have been investigated. Y zeolite crystals with high Si/Al ratios and small crystallite sizes were successfully synthesized by a new hydrothermal synthesis approach. The synthesized Y zeolite crystals were ion-exchanged and stabilized. The prepared samples were then modified with different gallium contents using an impregnation method to adjust their acidity properties, and these modified samples were used as co-supports for NiMo sulfide HDS catalysts. The catalyst containing 10 wt.% zeolite Y modified by 2 wt.% gallium (NiMo/2GaY-ASA-A) exhibited the highest HDS activity, with 4,6-dimethyldibenzothiophene (4,6-DMDBT) conversion nearly double the rate of the catalyst without zeolite at 563 K, 4.0 MPa and liquid hourly space velocity (LHSV) of 40 h . NiMo/2GaY-ASA-A also exhibited superior isomerization ability, with 3,4'-DMBP, 4,4'DMBP, and 3,6-DMDBT as the main products, indicating that the isomerization pathway was the main reaction route over NiMo/2GaY-ASA-A. The superior catalytic performance is related to the synergistic effect of the proper amount of medium and strong Brønsted acid sites. The compounds 3,6-DMDBT and 3,7-DMDBT (isomers of 4,6-DMDBT) and 3,4,6-TMDBT and tetra-methyl-DBT (transmethyl products) were detected simultaneously in the HDS product of 4,6-DMDBT for the first time over NiMo/GaY-ASA-A catalysts. Finally, a new reaction network over NiMo/2GaY-ASA-A was proposed.