Wide-area measurement systems enable the transmission of measurement and control signals for wide-area damping controllers (WADCs) in smart grids. However, the vulnerability of the communication network makes the WADC susceptible to malicious cyber attacks, such as false data injection (FDI) attack and denial of service (DoS) attack. Researchers develope numerous supervised machine-learning and model-based solutions for attack detection. However, the partially labeled attack data, skewed class distributions, and the need for precise mathematical models present significant challenges for real-world attack detection. This paper introduces the cyber attack-resilient wide-area damping controller (CyResWadc) system framework to address these challenges. The proposed framework leverages semi-supervised generative adversarial network (SSGAN) model to handle partially labeled attack data. It utilizes the support vector machine-based synthetic minority oversampling technique (SVM-SMOT) for data oversampling to manage skewed class distributions. Furthermore, probing signals are used to stimulate the power system, facilitating the generation of synthetic attack scenarios under different operational conditions. If any attack is detected, an alternate pair of measurement and control signals is used for attack mitigation. The performance is validated on a developed hardware-in-the-loop (HIL) cyber-physical testbed built using the open parallel architecture laboratory-real time (OPAL-RT) simulator, industry-grade hardware, Network Simulator 3 (NS-3), and open platform for data collection (OpenPDC).