While many FSCIL studies have been undertaken, achieving satisfactory performance, especially during incremental sessions, has remained challenging. One prominent challenge is that the encoder, trained with an ample base session training set, often underperforms in incremental sessions. In this study, we introduce a novel training framework for FSCIL, capitalizing on the generalizability of the Contrastive Language-Image Pre-training (CLIP) model to unseen classes. We achieve this by formulating image-object-specific (IOS) classifiers for the input images. Here, an IOS classifier refers to one that targets specific attributes (like wings or wheels) of class objects rather than the image's background. To create these IOS classifiers, we encode a bias prompt into the classifiers using our specially designed module, which harnesses key-prompt pairs to pinpoint the IOS features of classes in each session. From an FSCIL standpoint, our framework is structured to retain previous knowledge and swiftly adapt to new sessions without forgetting or overfitting. This considers the updatability of modules in each session and some tricks empirically found for fast convergence. Our approach consistently demonstrates superior performance compared to state-of-the-art methods across the miniImageNet, CIFAR100, and CUB200 datasets. Further, we provide additional experiments to validate our learned model's ability to achieve IOS classifiers. We also conduct ablation studies to analyze the impact of each module within the architecture.