  We study spin-half fermions in a one-dimensional extended Hubbard chain at
low filling. We identify three triplet and one singlet pairing channels in the
system, which are independently tunable as a function of nearest-neighbor
charge and spin interactions. In a large-size system with translational
invariance, we derive gap equations for the corresponding pairing gaps and
obtain a Bogoliubov-de Gennes Hamiltonian with its non-trivial topology
determined by the interplay of these gaps. In an open-end system with a fixed
number of particles, we compute the exact many-body ground state and identify
the dominant pairing revealed by the pair density matrix. Both cases show
competition between the four pairing states, resulting in broad regions for
each of them and relatively narrow regions for mixed-pairing states in the
parameter space. Our results enable the possibility of tuning a nanowire
between singlet and triplet pairing states without breaking time-reversal or
SU(2) symmetry, accompanied by a change in the system's topology.
