Handwritten character recognition is one of the classical problems in the field of image classification. Supervised learning techniques using deep learning models are highly effective in their application to handwritten character recognition. However, they require a large dataset of labeled samples to achieve good accuracies. Recent supervised learning techniques for Kannada handwritten character recognition have state of the art accuracy and perform well over a large range of input variations. In this work, a framework is proposed for the Kannada language that incorporates techniques from semi-supervised learning. The framework uses features extracted from a convolutional neural network backbone and uses regularization to improve the trained features and label propagation to classify previously unseen characters. The episodic learning framework is used to validate the framework. Twenty-four classes are used for pre-training, 12 classes are used for testing and 11 classes are used for validation. Fine-tuning is tested using one example per unseen class and five examples per unseen class. Through experimentation the components of the network are implemented in Python using the Pytorch library. It is shown that the accuracy obtained 99.13% make this framework competitive with the currently available supervised learning counterparts, despite the large reduction in the number of labeled samples available for the novel classes.