A viable alternative to the dark energy as a solution of the cosmic speed-up problem is represented by the Extended Theories of Gravity. Should this indeed be the case, there will be an impact that can be either on cosmological scales or on any scale, from the Solar system to the extragalactic ones. In particular, the gravitational potential can be different from the Newtonian one commonly adopted when computing the circular velocity fitted to spiral galaxies rotation curves. Phenomenologically modelling the modified point mass potential as the sum of a Newtonian and a Yukawa-like correction, we simulate the observed rotation curves for a spiral galaxy described as the sum of an exponential disc and a Navarro–Frenk–White (NFW) dark matter halo. We then fit these curves assuming parametrized halo models (either with an inner cusp or a core) and using the Newtonian potential to estimate the theoretical rotation curve. Such a study allows us to investigate the bias on the disc and halo model parameters induced by the systematic error that is induced by forcing the gravity theory to be Newtonian when it is not. As a general result, we find that both the halo scalelength and the virial mass are significantly overestimated, while the dark matter mass fraction within the disc optical radius is typically underestimated. Moreover, should the Yukawa scalelength be smaller than the disc half-mass radius, the logarithmic slope of the halo density profile would turn out to be shallower than the NFW one. Finally, cored models are able to fit quite well the simulated rotation curves, provided the disc mass is biased high in agreement with the results in literature, favouring cored haloes and maximal discs. Such results make us argue that the cusp/core controversy could actually be the outcome of an incorrect assumption about which theory of gravity must actually be used in computing the theoretical circular velocity.