  We study the phase diagram of quark matter at finite temperature and density
in the strong coupling lattice QCD with one species of unrooted staggered
fermions including finite coupling ($1/g^2$) effects for color SU($N_c$). We
find that we may have partially chiral restored medium density matter at
$N_c=3$, which would correspond to the quarkyonic matter suggested at large
$N_c$.
