  Recently, split-ring bosonic condensates of exciton polaritons have been
proposed for realisation of qubits. We formulate an analytical model of a
polariton condensate in a one-dimensional ring split by a delta-function
potential. The persistent current is stopped by the potential defect embedded
in a scalar condensate of non-interacting particles, however, it reappears in
the presence of an up-critical non-linearity. The nonlinear supercurrents are
characterised by fractional orbital momenta while their eigenfunctions may
feature grey or dark solitons. The coupling between the spin and the orbital
angular momentum of a spinor condensate affects persistent currents crucially.
We show that the spin-orbit interaction (SOI) induces the net superfluid
current in the condensate with a spatially uniform spin polarisation. We also
find solutions where the SOI-induced currents of two spin components of the
condensate propagate in opposite directions. The corresponding states of spinor
condensates obey a combined mirror reflection and the spin-flip symmetry.
