Doping Kondo lattice system CeRu2Si2 with Rh-8 % (Ce(Ru0.92Rh0.08)2Si2) leads to drastic consequences due to the mismatch of the lattice parameters between CeRu2Si2 and CeRh2Si2. A large variety of experiments clarifies the unusual properties of the ground state induced by the magnetic field from longitudinal antiferromagnetic (AF) mode at H = 0 to polarized paramagnetic phase in very high magnetic field. The separation between AF phase, paramagnetic phase and polarized paramagnetic phase varying with temperature, magnetic field and pressure is discussed on the basis of the experiments down to very low temperature. Similarities and differences between Rh and La substituted alloys are discussed with emphasis on the competition between transverse and longitudinal AF modes, and ferromagnetic fluctuations.