Two functional and positional candidate genes were selected in a region of chicken chromosome 1 (GGA1), based on their biological roles, and also where several quantitative trait loci (QTL) have been mapped and associated with performance, fatness and carcass traits in chickens. The insulin-like growth factor 1 (IGF1) gene has been associated with several physiological functions related to growth. The lysine (K)-specific demethylase 5A (KDM5A) gene participates in the epigenetic regulation of genes involved with the cell cycle. Our objective was to find associations of selected single-nucleotide polymorphisms (SNPs) in these genes with performance, fatness and carcass traits in 165 F(2) chickens from a resource population. In the IGF1 gene, 17 SNPs were detected, and in the KDM5A gene, nine SNPs were detected. IGF1 SNP c.47673G > A was associated with body weight and haematocrit percentage, and also with feed intake and percentages of abdominal fat and gizzard genotype × sex interactions. KDM5A SNP c.34208C > T genotype × sex interaction affected body weight, feed intake, percentages of abdominal fat (p = 0.0001), carcass, gizzard and haematocrit. A strong association of the diplotype × sex interaction (p < 0.0001) with abdominal fat was observed, and also associations with body weight, feed intake, percentages of carcass, drums and thighs, gizzard and haematocrit. Our findings suggest that the KDM5A gene might play an important role in the abdominal fat deposition in chickens. The IGF1 and KDM5A genes are strong candidates to explain the QTL mapped in this region of GGA1.