Supervised deep learning methods have achieved state-of-the-art performance on the task of named entity recognition (NER). However, such methods suffer from high cost and low efficiency in training data annotation, leading to highly specialized NER models that cannot be easily adapted to new domains. Recently, distant supervision has been applied to replace human annotation, thanks to the fast development of domain-specific knowledge bases. However, the generated noisy labels pose significant challenges in learning effective neural models with distant supervision. We propose PatNER, a distantly supervised NER model that effectively deals with noisy distant supervision from domain-specific dictionaries. PatNER does not require human-annotated training data but only relies on unlabeled data and incomplete domain-specific dictionaries for distant supervision. It incorporates the distant labeling uncertainty into the neural model training to enhance distant supervision. We go beyond the traditional sequence labeling framework and propose a more effective fuzzy neural model using the tie-or-break tagging scheme for the NER task. Extensive experiments on three benchmark datasets in two domains demonstrate the power of PatNER. Case studies on two additional real-world datasets demonstrate that PatNER improves the distant NER performance in both entity boundary detection and entity type recognition. The results show a great promise in supporting high quality named entity recognition with domain-specific dictionaries on a wide variety of entity types.