Convolutional neural networks (CNNs) models play a vital role in achieving state-of-the-art performances in various technological fields. CNNs are not limited to Natural Language Processing (NLP) or Computer Vision (CV) but also have substantial applications in other technological domains, particularly in cybersecurity. The reliability of CNN's models can be compromised because of their susceptibility to adversarial attacks, which can be generated effortlessly, easily applied, and transferred in real-world scenarios. In this paper, we present a novel and comprehensive method to improve the strength of attacks and assess the transferability of adversarial examples in CNNs when such strength changes, as well as whether the transferability property issue exists in computer network applications. In the context of our study, we initially examined six distinct modes of attack: the Carlini and Wagner (C&W), Fast Gradient Sign Method (FGSM), Iterative Fast Gradient Sign Method (I-FGSM), Jacobian-based Saliency Map (JSMA), Limited-memory Broyden fletcher Goldfarb Shanno (L-BFGS), and Projected Gradient Descent (PGD) attack. We applied these attack techniques on two popular datasets: the CIC and UNSW datasets. The outcomes of our experiment demonstrate that an improvement in transferability occurs in the targeted scenarios for FGSM, JSMA, LBFGS, and other attacks. Our findings further indicate that the threats to security posed by adversarial examples, even in computer network applications, necessitate the development of novel defense mechanisms to enhance the security of DL-based techniques.