Using social media, in particular, reading news articles, has become a necessary daily activity and an important way of spreading information. Classification of topics of new articles can provide up-to-date information about the current state of politics and society. However, this convenient way of sharing information can lead to the growth of falsification. Therefore, distinguishing between real and fake news, as well as fake-news classification, have become essential and indispensable. In this paper, we propose a new and up-to-date dataset for both fake-news classification and topic classification. To the best of our knowledge, we are the first to construct a dataset with both fake-news and topic labels, and employ multitask learning for learning these two tasks simultaneously. We have collected 21K online news articles published from January 2013 to March 2020. We propose an auxiliary-task long shortterm memory (AT-LSTM) neural network for text classification via multi-task learning. We evaluate and compare our proposed model to five baseline methods, via both single-task and multitask learning, on this new benchmark dataset. Experimental results show that our proposed AT-LSTM model outperforms the single-task learning methods and the hard parametersharing multi-task learning methods. The dataset and codes will be released in the future.