Study aim: The purpose of the study was to assess the level of physical fitness (PF) and somatic structure in children training a Korean martial art (ITF taekwondo) and untrained peers and to determine the associations of children’s BMI with that of their parents. Material and methods: The research material consisted of data from 135 individuals, representing 45 child-mother-father triplets, including 22 triplets with children practicing taekwondo and 23 triplets with untrained children. The children had an average chronological age of 10.08 ± 1.35 years, whereas the age of mothers and fathers was 38.09 ± 4.56 years and 40.57 ± 4.70 years, respectively. Traits analyzed included those evaluated by selected physical fitness tests from the Eurofit Physical Fitness Test battery, body mass index (BMI), and waist-to-height ratio (WHtR) in children, and BMI in parents. Statistical analyses included the chi-square test, Mann-Whitney U test, and Spearman’s correlations, with a significance level set at α = 0.05. Results: The results showed no significant differences in the somatic structure, physical fitness, BMI, and WHtR in the children studied. However, a tendency was observed for children attending ITF taekwondo classes to be characterized by higher levels of physical fitness. Higher BMI was found in the parents of the trained children and positive correlations were found between the BMI of the trained children and their parents. Conclusions: Identifying and studying the effect size of PA determinants in adolescents, with a particular focus on the influence of parents, may be the key to improving the health of future generations.