A continuous phase transition driven to zero temperature by a non-thermal parameter, such as pressure, terminates in a quantum critical point (QCP). At present, two main theoretical approaches are available for antiferromagnetic QCPs in heavy-fermion systems. The conventional one is the quantum generalization of finite-temperature phase transitions, which reproduces the physical properties in many cases(1-5). More recent unconventional models incorporate a breakdown of the Kondo effect, giving rise to a Fermi-surface reconstruction(6-8)-YbRh2Si2 is a prototype of this category(5,9-11). In YbRh2Si2, the antiferromagnetic transition temperature merges with the Kondo breakdown at the QCP. Here, we study the evolution of the quantum criticality in YbRh2Si2 under chemical pressure. Surprisingly, for positive pressure we find the signature of the Kondo breakdown within the magnetically ordered phase, whereas negative pressure induces their separation, leaving an intermediate spin-liquid-type ground state over an extended range. This behaviour suggests a new quantum phase arising from the interplay of the Kondo breakdown and the antiferromagnetic QCP.