Class-conditional GAN generates class-conditional data from continuous latent distribution and categorical distribution. Typically, a class-conditional GAN can be trained only when the label, which is the conditional categorical distribution of the target data, is given. In this paper, we propose a novel GAN that allows the model to perform self-supervised class-conditional data generation and clustering without knowing labels, optimal prior categorical probability, or metric function. The proposed method uses a discriminator, a classifier, and a generator. The classifier is trained with cross-entropy loss to predict the conditional vector of the fake data. Also, the conditional vector of real data predicted by the classifier is used to train the class-conditional GAN. When training class-conditional GAN with this classifier, the decision boundary of the classifier falls to the local optima where the density of the data is minimized. The proposed method adds a classifier gradient penalty loss to the classifier loss to prevent the classifier's decision boundary from falling into narrow a range of local optima. It regulates the gradient of the classifier's output to prevent the gradient near the decision boundary from becoming too large. As the classifier gradient penalty loss weight increases, the decision boundary falls into a wider range of local optima. It means that the sensitivity of each class can be adjusted by the weight of the gradient penalty loss. Additionally, the proposed method updates the prior categorical probability with the categorical probability of real data predicted by the classifier. As training progresses, the entropy of the prior categorical probability decreases and converges according to the classifier gradient penalty loss weight.