The aim of this study is to identify the most suitable model for fitting data related to some milk traits, including total milk yield (TMY) and lactation period (LP) and prolificacy traits, including the number of kids born (NKB) and the number of kids weaned (NKW). The models under consideration varied based on the absence or presence of additive and maternal genetic effects, permanent environmental effect, and the direct-maternal genetic covariance (σam). The dataset comprised 1638 kidding records from 411 does and 79 bucks. Statistical analyses were performed using the MTDFREML software, with model selection guided by the Akaike information criterion (AIC). Across all examined models, direct heritabilities ranged from 0.258 to 0.375 for TMY, 0.172 to 0.252 for LP, 0.220 to 0.265 for NKB, and 0.074 to 0.133 for NKW. Corresponding maternal heritabilities estimates varied from 0.094 to 0.144, 0.089 to 0.112, 0.078 to 0.097, and 0.043 to 0.080, respectively. Direct-maternal genetic correlations were positive form milk traits (0.123 for TMY and 0.093 for LP) and negative for prolificacy traits (-0.261 for NKB and -0.082 for NKW). Genetic, maternal, and phenotypic correlation were positive between studied traits. Additionally, a wide range of breeding values was noted among sires for TMY, LP, and NKB. In conclusion, it is advised to incorporate both direct and maternal effects, and their covariance in statistical models for optimal genetic improvement of Zaraibi goats in Egypt.