The contextual bandit has been identified as a powerful framework to formulate the recommendation process as a sequential decision-making process, where each item is regarded as an arm and the objective is to minimize the regret of $T$ rounds. In this paper, we study a new problem, Clustering of Neural Bandits, by extending previous work to the arbitrary reward function, to strike a balance between user heterogeneity and user correlations in the recommender system. To solve this problem, we propose a novel algorithm called M-CNB, which utilizes a meta-learner to represent and rapidly adapt to dynamic clusters, along with an informative Upper Confidence Bound (UCB)-based exploration strategy. We provide an instance-dependent performance guarantee for the proposed algorithm that withstands the adversarial context, and we further prove the guarantee is at least as good as state-of-the-art (SOTA) approaches under the same assumptions. In extensive experiments conducted in both recommendation and online classification scenarios, M-CNB outperforms SOTA baselines. This shows the effectiveness of the proposed approach in improving online recommendation and online classification performance.