We explore the structural properties of anomalous fluids confined in a nanopore using molecular dynamics simulations. The fluid is modeled by core-softened (CS) potentials that have a repulsive shoulder and an attractive well at a further distance. Changing the attractive well depth of the fluidfluid interaction potential, we studied the behavior of the anomalies in the translational order parameter t and excess entropy s(2) for the particles near to the nanopore wall (contact layer) for systems with two or three layers of particles. When the attractive well of the CS potential is shallow, the systems present a three to two layers transition and, additionally to the usual structural anomaly, a new anomalous region in t and s(2). For attractive well deep enough, the systems change from three layers to a bulk-like profile and just one region of anomaly in t and s(2) is observed. Our results are discussed on the basis of the fluidfluid and fluid-surface interactions.