Recently, neural networks based on multi-task learning have achieved promising performance on fake news detection, which focuses on learning shared features among tasks as complementarity features to serve different tasks. However, in most of the existing approaches, the shared features are completely assigned to different tasks without selection, which may lead to some useless and even adverse features integrated into specific tasks. In this paper, we design a sifted multi-task learning method with a selected sharing layer for fake news detection. The selected sharing layer adopts gate mechanism and attention mechanism to filter and select shared feature flows between tasks. Experiments on two public and widely used competition datasets, i.e. RumourEval and PHEME, demonstrate that our proposed method achieves the state-of-the-art performance and boosts the F1-score by more than 0.87%, 1.31%, respectively.