In mesoscopic superconductors with low intrinsic pinning, the boundary plays the most important role in the stabilization of the vortex patterns. Especially in the case of symmetric sample shape, very distinct vortex locations inside the sample are defined, for the different vorticity states. The study of two-component superconductors with the Ginzburg-Landau equation implies the introduction of a coupling term between the two condensates, changing the linear part of the potential. This article presents the analysis of the impact of the competition between the coupling term and the geometry of confinement on the vortex patterns of thin mesoscopic square samples made from a two-gap superconductor. For a simple case presented here, it was found that the appearance of the noncomposite vortices is accompanied by an unusual shape of the component of the order parameter associated with the passive band as a function of the temperature. This shape is a distinct fingerprint for materials with noncomposite vortices.