Assessing dominance and additive effects of casein complex single-nucleotide polymorphisms (SNPs) (αS1, αS2, β, and κ casein), and their epistatic relationships may maximize our knowledge on the genetic regulation of profitable traits. Contextually, new genomic selection perspectives may translate this higher efficiency into higher accuracies for milk yield and components’ genetic parameters and breeding values. A total of 2594 lactation records were collected from 159 Murciano-Granadina goats (2005–2018), genotyped for 48 casein loci-located SNPs. Bonferroni-corrected nonparametric tests, categorical principal component analysis (CATPCA), and nonlinear canonical correlations were performed to quantify additive, dominance, and interSNP epistatic effects and evaluate the outcomes of their inclusion in quantitative and qualitative milk production traits’ genetic models (yield, protein, fat, solids, and lactose contents and somatic cells count). Milk yield, lactose, and somatic cell count heritabilities increased considerably when the model including genetic effects was considered (0.46, 0.30, 0.43, respectively). Components standard prediction errors decreased, and accuracies and reliabilities increased when genetic effects were considered. Conclusively, including genetic effects and relationships among these heritable biomarkers may improve model efficiency, genetic parameters, and breeding values for milk yield and composition, optimizing selection practices profitability for components whose technological application may be especially relevant for the cheese-making dairy sector.