  We report the discovery of new superconducting and novel magnetic phases in
CeIn$_3$ on the verge of antiferromagnetism (AFM) under pressure ($P$) through
the In-nuclear quadrupole resonance (NQR) measurements. We have found a
$P$-induced phase separation of AFM and paramagnetism (PM) without any trace
for a quantum phase transition in CeIn$_3$. A new type of superconductivity
(SC) was found in $P=2.28-2.5$ GPa to coexist with AFM that is magnetically
separated from PM where the heavy fermion SC takes place. We propose that the
magnetic excitations such as spin-density fluctuations induced by the
first-order magnetic phase transition might mediate attractive interaction to
form Cooper pairs.
