The transmission of medical images via medical agencies raises security concerns, necessitating increased security measures to ensure integrity and security. However, many watermarking algorithms overlook equipoise; the relation between robustness, invisibility, and payload capacity results in a less satisfactory performance. To bridge this gap, we propose a new blind watermarking method for securing medical images based on a convolutional neural network in a fusion domain. First, we transmute the host color image using a phase-only transform (PHOT) to detect the surface pattern. We feed the detected surface pattern into a pre-trained VGG19 model to impeccably extract the stable feature vector. We encrypt the extracted image features using a hybrid Chirikov map to enhance their robustness and reliability. The synergy between the pre-trained VGG19 model and PHOT in an integrated domain effectively captures additional native and localized image features. A hybrid Fibonacci Q-matrix method scrambles the binary watermark to enhance security. Integrating double encryption into the proposed method markedly enhances its resistance against diverse countermeasures. Experimental outcomes indicate that the proposed scheme performs efficiently in robustness and invisibility. The obtained PSNR value was up to 60.15 dB, which is optimal for human perception. The embedded watermark can be retrieved without any warping. The retrieved watermark seems to be authentic, exhibiting ideal BER and NC values. In almost all attack circumstances, the BER values approached zero while the NC values got closer. The proposed method demonstrates notable enhancements in robustness and invisibility compared to prior methods.