In real world scenarios where we use machine learning algorithms, we often have to deal with cases where input data changes its nature with time. In order to maintain the accuracy of the learning algorithm, we frequently have to retrain our learning system, thereby making the system inconvenient and unreliable. This problem can be solved by using learning algorithms which can learn continuously with time (incremental/ online learning). Another common problem of real-world learning scenarios that we often have to deal with is acquiring large amounts of data which is expensive and time consuming. Semi-supervised learning is the machine learning paradigm concerned with utilizing unlabeled data to improve the precision of classifier or regressor. Unlabeled data is a powerful and easily available resource and it should be utilized to build an accurate learning system. It has often been observed that there is a vast amount of redundancy in any huge, real-time database and it is not advisable to process every redundant sample to gain the same (already acquired) knowledge. Active learning is the learning setting which can handle this issue. Therefore in this research we propose an online semi-supervised learning framework which can learn actively. We have proposed an "online semi-supervised Random Naive Bayes (RNB)" classifier and as the name implies it can learn in an online manner and make use of both labeled and unlabeled data to learn. In order to boost accuracy we improved the network structure of NB (using Bayes net) to propose an Augmented Naive Bayes (ANB) classifier and achieved a substantial jump in accuracy. In order to reduce the processing of redundant data and achieve faster convergence of learning, we proposed to conduct incremental semi-supervised learning in active manner. We applied the proposed methods on the "Tamil script handwritten character recognition" problem and have obtained favorable results. Experimental results prove that our proposed online classifiers does as well as and sometimes better than its batch learning counterpart. And active learning helps to achieve learning convergence with much less number of samples.