In the realm of secure digital communication, balancing payload capacity with perceptual imperceptibility remains a critical challenge, particularly within lossy compression standards like JPEG. This paper proposes a robust steganography framework that addresses this trade-off by integrating adaptive Discrete Cosine Transform (DCT) modification with an edge-based selection criterion. Unlike uniform embedding approaches that indiscriminately treat all image regions, the proposed method employs Canny edge detection to categorize blocks based on texture complexity. This strategy leverages the masking properties of the Human Visual System (HVS), allocating higher payload capacities to complex, edge-rich regions where modifications are statistically less detectable. To further enhance embedding efficiency, a decimal-to-ternary (base-3) coding scheme is introduced to optimize the utilization of DCT coefficients. This mechanism is coupled with a modulo optimization search within a constrained range of , which minimizes the magnitude of necessary modifications compared to traditional binary embedding. Experimental evaluations on standard datasets, including USC-SIPI, indicate that the method maintains a Peak Signal-to-Noise Ratio (PSNR) significantly higher than traditional methods, ranging from 48 dB to 62 dB depending on the embedding rate. Furthermore, quantitative analysis demonstrates a 58.5% improvement in embedding efficiency over standard binary techniques. Consequently, this adaptive strategy offers a superior trade-off between high-capacity data hiding and resistance to statistical steganalysis compared to standard LSB and non-adaptive DCT methods.