  In this paper we investigate the cutoff effects at tree-level of perturbation
theory for three different lattice regularizations of fermions -- maximally
twisted mass Wilson, overlap and Creutz fermions. We show that all three kinds
of fermions exhibit the expected $O(a^2)$ scaling behaviour in the lattice
spacing. Moreover, the size of these cutoff effects for the considered
quantities i.e. the pseudoscalar correlation function $C_{PS}$, the mass
$m_{PS}$ and the decay constant $f_{PS}$ is comparable for all of them.
