An experimental evidence of the progressive modification in the magnetic behavior of granular Fe/Si3N4 samples due to interaction effects between particles is reported. Microstructural features and local structure were determined by x-ray absorption spectroscopy and transmission electron microscopy to select granular samples with predetermined cluster size. Fe/Si3N4 systems have been characterized by ac- and demagnetization measurements to study the gradual evolution of magnetic properties of granular systems, where three different behaviors have been observed. As-deposited samples with Fe thickness layers of 2.5 nm, present a modified superparamagnetic behavior, due to very weak interactions between very small Fe clusters separated by a nonmagnetic FeN phase. An evolution of the average blocking temperature at intermediate fields (T-B similar to H-3/2) is observed, similar to noninteracting systems, but first signatures of a frozen spin state at low temperatures appear. Annealed samples exhibit a noticeable modification from the multilayer character to a random three-dimensional organization of Fe clusters embedded in a Si3N4 matrix. After annealing, samples with initial Fe layer thickness of 0.7 nm provide iron cluster in the range of 1.3 nm and exhibit a superspin-glass state, with a de Almeida-Thouless evolution of the energy barriers (T-B similar to H-2/3) that is explained in terms of increasing interparticle interactions. Moreover, annealed samples, with initial layer thickness of 1.3 nm, supply iron cluster of near 3 nm that present stronger interactions and yield a superferromagnetic state, likely provided by residual ultrasmall particles between the blocked clusters.