The progression of genetic selection techniques to enhance farm animal performance traits is guided by the present level of genetic variation and maternal impact in each trait, as well as the genetic association between traits. This study was conducted on a population of Mecheri sheep maintained from 1980 to 2018 at Mecheri Sheep Research Station, Pottaneri, India, to determine variance and covariance components, as well as genetic parameters for various production performance traits. A total of 2616 lambs, produced by 1044 dams and 226 sires, were examined in the study and the production traits of Mecheri sheep assessed include birth weight (BW), weaning weight (WW), six-month weight (SMW), nine-month weight (NMW), and yearling weight (YW). The Bayesian approach, using the Gibbs sampler, analyzed six animal models with different combinations of additive direct and maternal additive effects. Direct genetics, maternal genetics, and residual effects models were the major contributors to total phenotypic variation for all the production traits studied. Direct heritability estimates of birth weight, WW, SMW, NMW, and YW were 0.25, 0.20, 0.12, 0.14, and 0.13, respectively. The maternal heritability estimated for BW, WW, SMW, NMW, and YW were 0.17, 0.10, 0.12, 0.14, and 0.14, respectively. The maternal effects had a major impact on the pre-weaning production traits. The genetic correlations estimated between different pairs of production traits studied ranged from 0.19 to 0.93. The body weight at birth exhibited a higher genetic relationship with weaning weight than post-weaning growth characteristics, and the genetic correlation between weaning weight and post-weaning attributes was moderate to high (0.52 to 0.72). Based on the additive genetic variance in weaning weight and the correlation estimates of weaning weight with post-weaning traits, weaning weight was proposed as a selection criterion for improving growth traits in Mecheri sheep.