  We deal with the question of what it means to define a minimal coupling
prescription in presence of torsion and/or non-metricity, carefully explaining
while the naive substitution $\partial\to\na$ introduces extra couplings
between the matter fields and the connection that can be regarded as
non-minimal in presence of torsion and/or non-metricity. We will also
investigate whether minimal coupling prescriptions at the level of the action
(MCPL) or at the level of field equations (MCPF) lead to different dynamics. To
that end, we will first write the Euler-Lagrange equations for matter fields in
terms of the covariant derivatives of a general non-Riemannian space, and
derivate the form of the associated Noether currents and charges. Then we will
see that if the minimal coupling prescriptions is applied as we discuss, for
spin 0 and 1 fields the results of MCPL and MCPF are equivalent, while for spin
1/2 fields there is a difference if one applies the MCPF or the MCPL, since the
former leads to charge violation.
