Domestication of teleost fish is a recent development, and in most cases started less than 50 years ago. Shedding light on the genomic changes in key economic traits during the domestication process can provide crucial insights into the evolutionary processes involved and help inform selective breeding programmes. Here we report on the recent domestication of a native marine teleost species in New Zealand, the Australasian snapper (Chrysophrys auratus). Specifically, we use genome-wide data from a three-generation pedigree of this species to uncover genetic signatures of domestication selection for growth. Genotyping-By-Sequencing (GBS) was used to generate genome-wide SNP data from a three-generation pedigree to calculate generation-wide averages of FST between every generation pair. The level of differentiation between generations was further investigated using ADMIXTURE analysis and Principal Component Analysis (PCA). After that, genome scans using Bayescan, LFMM and XP-EHH were applied to identify SNP variants under putative selection following selection for growth. Finally, genes near candidate SNP variants were annotated to gain functional insights. Analysis showed that between generations FST values slightly increased as generational time increased. The extent of these changes was small, and both ADMIXTURE analysis and PCA were unable to form clear clusters. Genome scans revealed a number of SNP outliers, indicative of selection, of which a small number overlapped across analyses methods and populations. Genes of interest within proximity of putative selective SNPs were related to biological functions, and revealed an association with growth, immunity, neural development and behaviour, and tumour repression. Even though few genes overlapped between outlier SNP methods, gene functionalities showed greater overlap between methods. While the genetic changes observed were small in most cases, a number of outlier SNPs could be identified, of which some were found by more than one method. Multiple outlier SNPs appeared to be predominately linked to gene functionalities that modulate growth and survival. Ultimately, the results help to shed light on the genomic changes occurring during the early stages of domestication selection in teleost fish species such as snapper, and will provide useful candidates for the ongoing selective breeding in the future of this and related species.