A chain or belt tensioning roller or winder device having a rolling bearing, the rolling bearing comprising an inner ring, an outer ring and at least one row of rolling elements mounted between the rings. The pulley is overmolded onto the outer ring and with a fixing screw axially immobilized with respect to the rolling bearing. The device comprises a sleeve overmolded inside the bore of the inner ring and provided with a through-bore for mounting the fixing screw. The sleeve is provided with means of axially retaining the fixing screw inside the through-bore of the sleeve.