  We investigate the emergence and corresponding nature of exceptional points
located on exceptional hyper-surfaces of non-hermitian transfer matrices for
finite-range one-dimensional lattice models. We unravel the non-trivial role of
these exceptional points in determining the system size scaling of electrical
conductance in non-equilibrium steady state. We observe that the band edges of
the system always correspond to the transfer matrix exceptional points.
Interestingly, albeit the lower band edge always occurs at wave-vector $k=0$,
the upper band edge may or may not correspond to $k=\pi$. Nonetheless, in all
the cases, the system exhibits universal subdiffusive transport for conductance
at every band edge with scaling $N^{-b}$ with scaling exponent $b= 2$. However,
for cases when the upper band edge is not located at $k=\pi$, the conductance
features interesting oscillations with overall $N^{-2}$ scaling. Our work
further reveals that this setup is uniquely suited to systematically generate
higher order transfer matrix exceptional points at upper band edge when one
considers finite range hoppings beyond nearest neighbour. Additional
exceptional points other than those at band edges are shown to occur, although
interestingly, these do not give rise to anomalous transport.
