Background: Childhood obesity is associated with important alterations in body composition that may impair muscular strength and functional capacity. While higher body mass is often accompanied by greater absolute strength, the independent impact of adiposity on muscular strength after accounting for lean tissue remains insufficiently understood. The aim of this study was to examine the associations between adiposity, body composition, and muscular strength in children and adolescents, with particular focus on the independent effects of fat mass after adjustment for growth- and maturation-related factors. Methods: This cross-sectional study included 84 children and adolescents aged 5–18 years. Anthropometric measurements were used to calculate body mass index, waist-to-hip ratio, and waist-to-height ratio, with weight status classified according to World Health Organization BMI-for-age criteria. Body composition was assessed using bioelectrical impedance analysis (Tanita), providing estimates of body fat percentage and Tanita-derived muscle mass. Pubertal stage was assessed using Tanner classification. Muscular strength was evaluated using dominant handgrip strength, and habitual physical activity was recorded as hours per week. Associations between adiposity-related indices and muscular strength were explored using correlation and multiple linear regression analyses, with adjustment for age and Tanita-derived muscle mass. Results: Body mass index showed a positive association with handgrip strength, reflecting the contribution of overall body mass. Central adiposity indices demonstrated weak to modest associations with muscular strength. Body fat percentage showed only a limited association with handgrip strength in unadjusted analyses. However, in multivariable regression models adjusting for age and Tanita-derived muscle mass, higher body fat percentage emerged as an independent negative predictor of handgrip strength. Age did not show an independent association with muscular strength in adjusted models. Conclusions: Excess adiposity is independently and negatively associated with muscular strength in children and adolescents, even after accounting for age and Tanita-derived estimates of muscle mass. These findings suggest that increased fat mass may impair neuromuscular performance beyond its effects on body size or lean tissue. Pediatric obesity interventions should therefore focus not only on weight reduction but also on improving body composition and preserving functional strength.