  The onset of the pseudogap in high-$T_c$ superconducting cuprates (HTSC) is
marked by the $T^*$ line in the doping-temperature phase diagram, which ends at
a point $p^*$ at zero temperature within the superconducting dome. Although
various theoretical and experimental studies indicate a competition between the
pseudogap and superconductivity, there is no general consensus on the effects
of the pseudogap within the superconducting phase. We use cluster dynamical
mean field theory on a three-band Hubbard model for the HTSC to study the
superconducting phase at $T=0$, obtained when doping the charge-transfer
insulator, for several values of $U$. We observe a first-order transition
within the superconducting phase, which separates the underdoped and overdoped
solutions. The transition to the underdoped solution is marked by a
discontinuous increase in the spectral gap, and on further underdoping the
spectral gap increases while the superconducting order parameter decreases. We
conclude that this is due to the onset of the pseudogap in the underdoped
region, which contributes to the increasing spectral gap; this is further
consistent with the appearance of a pole in the normal component of the
self-energy, in the antinodal region, in the underdoped solution. This is
accompanied by a change in the source of the condensation energy from potential
energy, in the overdoped region, to kinetic energy in the underdoped region.
Further, we also observe that the $d$-wave node vanishes smoothly within the
superconducting phase at low values of hole doping, within the underdoped
region. We see this as a manifestation of Mott physics operating at very low
doping. Various aspects of the results and their implications are discussed.
