  The issue of whether the quantum critical point (QCP) is hidden inside
unconventional superconductors is a matter of hot debate. Although a prominent
experiment on London penetration depth has demonstrated the existence of the
QCP in the isovalent-doped iron-based superconductor
BaFe$_2$(As$_{1-x}$P$_x$)$_2$, with the observation of a sharp peak in the
penetration depth in the vicinity of the disappearance of magnetic order at
zero temperature, the nature of such an emerging QCP remains unclear. Here, we
provide a unique picture to understand well the phenomena of the QCP based on
the framework of linear response theory. Evidence from the density of states
and superfluid density calculations suggests the nodeless-to-nodal pairing
transition accompanied the appearance of a sharp peak in the penetration depth
in BaFe$_2$(As$_{1-x}$P$_x$)$_2$. Such a pairing transition originates from the
three-dimensional electronic properties with a strong interlayer
superconducting pairing. This finding provides a significant insight into the
understanding of the QCP observed in experiment in
BaFe$_2$(As$_{1-x}$P$_x$)$_2$.
