No, a positron is a lepton but a neutron is not. Since lepton number must be conserved, these two will not annihilate with each other. Similarly, one has a positive charge and the other neutral, so electric charge would not be conserved either.
Are you thinking of a neutron plus an antiproton? Those can annihilate with each other. They are not direct antiparticles of each other, but the neutron is really an up quark and two down quarks, while the antiproton is really two anti–up quarks and an anti–down quark. There are several different ways that they could annihilate with each other.
Worse, all hadrons (like neutrons and protons) contain a confined gluon field which you can think of as containing additional quark–antiquark pairs. There’s a chance that the gluon fields of the two particles will interact as if a quark–antiquark pair from one had annihilated with a quark–antiquark pair from the other, further complicating the results. This can cause the creation of other exotic particles as the quarks combine and recombine.
Are you thinking of a neutron plus an antiproton? Those can annihilate with each other. They are not direct antiparticles of each other, but the neutron is really an up quark and two down quarks, while the antiproton is really two anti–up quarks and an anti–down quark. There are several different ways that they could annihilate with each other.
Worse, all hadrons (like neutrons and protons) contain a confined gluon field which you can think of as containing additional quark–antiquark pairs. There’s a chance that the gluon fields of the two particles will interact as if a quark–antiquark pair from one had annihilated with a quark–antiquark pair from the other, further complicating the results. This can cause the creation of other exotic particles as the quarks combine and recombine.
You can read more about it on Wikipedia, of course: https://en.wikipedia.org/wiki/Annihilation