  We investigate the impact of s-wave spin-singlet pairing on antiferromagnetic
semimetals with Dirac points or nodal loops at the Fermi level. The electron
pairing is generally shown to convert the semimetal into a tunable nodal
superconductor. The changeover from fully gapped to gapless phases is dictated
by symmetry properties of the antiferromagnetic-superconducting state that set
the occurrence of a large variety of electronic topological transitions. We
provide a general criterion for predicting a series of transitions between
nodal and fully gapped superconducting phases. Different types of
antiferromagnetic patterns are then employed to explicitly demonstrate the
microscopic mechanisms that control the character of the quasiparticle
spectrum. These findings unveil a novel type of nodal superconductivity
emerging from the interplay of Dirac fermions and conventional forms of
ordering.
