  Hadronic matrix elements evaluated on the lattice can be converted to a
continuum scheme such as $\MSbar$ using intermediate non-perturbative
renormalisation schemes. Discretisation effects on the lattice and convergence
of the continuum perturbation theory are both scheme dependent and we explore
this dependence in the framework of the Rome-Southampton method for generalised
kinematics. In particular, we implement several non-exceptional {\em
interpolating} momentum schemes, where the momentum transfer is {\em not}
restricted to the symmetric point defined in RI/SMOM. Using flavour non-singlet
quark bilinears, we compute the renormalisation factors of the quark mass and
wave function for $N_f=3$ flavours of dynamical quarks. We investigate the
perturbative and non-perturbative scale-dependencies. Our numerical results are
obtained from lattice simulations performed with Domain-Wall fermions, based on
ensembles generated by RBC-UKQCD collaborations; we use two different lattice
spacings $1/a \sim 1.79 $ and $2.38$ GeV. We also give the numerical values for
the relevant anomalous dimensions and matching coefficients at
next-to-next-to-leading order.
