The competition between magnetic ordering and the Kondo effect in Ce2RhSi3, ordering antiferromagnetically at 7 K, is investigated by the measurements of magnetization, heat capacity and electrical resistivity on the solid solutions, Ce(2-x)La(x)RhSi3, Ce(2-y)Y(y)RhSi3, and Ce2RhSi(3-z)Ge(z), as well as by high pressure studies on this compound. The trends in the Kondo and Neel temperature variations among these alloys are compared to infer the roles of unit-cell volume and electronic structure changes. On the basis of the results, we infer that this compound lies at the peak of Doniach-magnetic-phase-diagram. The high pressure electrical resistivity data indicate that the quantum critical point for this compound is in the vicinity of 4 GPa.