  The Pfaffian fractional quantum Hall (FQH) states are incompressible
non-Abelian topological fluids present in a half-filled electron Landau level,
where there is a balanced population of electrons and holes. They give rise to
half-integral quantum Hall plateaus that divide critical transitions between
integer quantum Hall (IQH) states. On the other hand, there are Abelian FQH
states, such as the Laughlin state, that can be understood using partons, which
are fermionic divisions of the electron. In this paper, we propose a new family
of incompressible paired parton FQH states at filling $\nu=1/6$ (modulo 1) that
emerge from critical transitions between IQH states and Abelian FQH states at
filling $\nu=1/3$ (modulo 1). These paired parton states are originated from a
half-filled parton Landau level, where there is an equal amount of partons and
holes. They generically support Ising-like anyonic quasiparticle excitations
and carry non-Abelian Pfaffian topological orders (TO) for partons. We prove
the principle existence of these paired parton states using exactly solvable
interacting arrays of electronic wires under a magnetic field. Moreover, we
establish a new notion of particle-hole (PH) symmetry for partons and relate
the PH symmetric parton Pfaffian TO with the gapped symmetric surface TO of a
fractional topological insulator in three dimension.
