  We study the isovalent substitution effect by partially introducing Se on S
site in the newly discovered superconductor Nb$_2$PdS$_5$ ($T_c\sim$6 K) whose
upper critical field is found to be far above its Pauli paramagnetic limit. In
this Nb$_2$Pd(S$_{1-x}$Se$_x$)$_5$ (0$\leq$$x$$\leq$0.8) system,
superconductivity is systematically suppressed by the Se concentration and
ultimately disappears when $x\geq$ 0.5, after which a semiconducting-like
ground state emerges. In spite of the considerably reduced $T_c$ with Se
doping, the ratio of the upper critical field $H_{c2}$ to $T_c$, remains
unaffected. Moreover, the size of the heat capacity jump at $T_c$ is smaller
than that expected for a BCS superconductor, implying that a strong-coupling
theory cannot be the origin of this large upper critical field. In addition,
the low-lying quasiparticle excitations are consistent with a nodeless gap
opening over the Fermi surface. These results combined impose severe
constraints on any theory of exotic superconductivity in this system.
