  The singlet s-, d- and triplet p-wave pairing symmetries in
quasi-one-dimensional organic superconductors can be experimentally
discriminated by probing the Andreev bound states at the sample edges. These
states have the energy in the middle of the superconducting gap and manifest
themselves as a zero-bias peak in tunneling conductance into the corresponding
edge. Their existence is related to the sign change of the pairing potential
around the Fermi surface. We present an exact self-consistent solution of the
edge problem showing the presence of the midgap states for p_x-wave
superconductivity. The spins of the edge state respond paramagnetically to a
magnetic field parallel to the vector d that characterizes triplet pairing.
