Let k be an algebraically closed field. In characteristic 2, the isolated wild quotient singularities arising from an action of the cyclic group Z/2Z on the power series ring in two variables k[[u, v]], were completely described by Artin as an explicit hypersurface singularity. Peskin extended Artin’s result in characteristic 3. Moreover, she developed canonical forms for certain p-cyclic automorphism of formal power series rings over fields in positive characteristic. More recently, Schröer and Lorenzini introduced moderately ramified actions in any characteristic p > 0 on the formal power series ring k[[u_1, . . . , u_n]] with n ≥ 2, which give rise to a new class of wild quotient singularities. Motivated by this construction, we will describe in this talk the resolution of singularities of the singularity arising from the moderately ramified action on k[[u, v]] in a particular case and we aim to compute the cohomology of the structure sheaf of this resolution which is an invariant of this singularity.