Adversarial transferability remains a critical challenge in evaluating the robustness of deep neural networks. In security-critical applications, transferability enables black-box attacks without access to model internals, making it a key concern for real-world adversarial threat assessment. While Vision Transformers (ViTs) have demonstrated strong adversarial performance, existing attacks often fail to transfer effectively across architectures, especially from ViTs to Convolutional Neural Networks (CNNs) or hybrid models. In this paper, we introduce \textbf{TESSER} -- a novel adversarial attack framework that enhances transferability via two key strategies: (1) \textit{Feature-Sensitive Gradient Scaling (FSGS)}, which modulates gradients based on token-wise importance derived from intermediate feature activations, and (2) \textit{Spectral Smoothness Regularization (SSR)}, which suppresses high-frequency noise in perturbations using a differentiable Gaussian prior. These components work in tandem to generate perturbations that are both semantically meaningful and spectrally smooth. Extensive experiments on ImageNet across 12 diverse architectures demonstrate that TESSER achieves +10.9\% higher attack succes rate (ASR) on CNNs and +7.2\% on ViTs compared to the state-of-the-art Adaptive Token Tuning (ATT) method. Moreover, TESSER significantly improves robustness against defended models, achieving 53.55\% ASR on adversarially trained CNNs. Qualitative analysis shows strong alignment between TESSER's perturbations and salient visual regions identified via Grad-CAM, while frequency-domain analysis reveals a 12\% reduction in high-frequency energy, confirming the effectiveness of spectral regularization.