The control of laser-induced microcracks in the volume of transparent materials is essential for scribing processes. In this paper, we investigate the effect of various amplitude and single-level phase masks on both transverse and axial intensity distribution of the conventional axicon-generated Bessel beams. Furthermore, we demonstrate the volumetric crack control induced by an asymmetrical central core with an appropriately selected intensity level to avoid the influence of peripheral intensity maxima. Proper alignment of cracks and intra-distance between the modifications results in the reduced separation stress of the scribed samples. Furthermore, the additional amplitude modulation of the incident Gaussian beam is introduced to flatten the axial intensity distribution of the axicon-generated Bessel beam.