  We report a pressure ($P$) effect on CeCu$_2$(Si$_{0.98}$Ge$_{0.02}$)$_2$
where an antiferromagnetic (AFM) order at $T_N \sim$ 0.75 K coexists with
superconductivity below $T_c \sim$ 0.4<EMAIL_ADDRESS>At pressures exceeding $P = 0.19$
GPa, the AFM order is suppressed, which demonstrates that the sudden emergence
of AFM order due to the Ge doping is ascribed to the intrinsic lattice
expansion. The exotic superconductivity at $P = 0$ GPa is found to evolve into
a typical heavy-fermion one with a line-node gap above $P = 0.91$<EMAIL_ADDRESS>We
highlight that the anomalous enhancement in nuclear spin-lattice relaxation
rate $1/T_1$ that follows a $T_1T$ = const. behavior well below $T_c$ at $P$ =
0 GPa is characterized by the persistence of low-lying magnetic excitations,
which may be inherent to the coexistent state of antiferromagnetism and
superconductivity.
