This work broadens fixed point (FP) theory by introducing results within the setting of digital parametric metric spaces (DPMS). Motivated by the discrete nature of digital data and the flexibility offered by parametric distance measures, we treat a DPMS as a structure in which separation between points is evaluated through a digitally defined metric that depends on a positive parameter. Several new FP results are established aimed at self-mappings on such spaces, and their applicability is illustrated in contexts such as computational geometry, discrete dynamical systems, and digital image analysis. The convergence patterns of iteratively generated sequences are explored under suitable contractive conditions, supporting the theoretical developments. In addition to enriching the theory of fixed points in discrete spaces, these results create potential avenues for use in problems requiring digital computation and structured data processing.