The rich development ecosystem of Python provides a lot of third-party libraries, significantly boosting developers' efficiency and quality. Third-party library developers encapsulate underlying code, enabling upper-layer application developers to swiftly accomplish tasks by calling relevant APIs. However, APIs of third-party libraries are not constant. Owing to fixes, refactoring, and feature additions, these libraries undergo continuous updates. Incompatible changes are seen in some APIs after updates, leading to abnormal termination or inconsistent results in upper-layer applications. Therefore, the API compatibility of the Python third-party library has become one of the issues that needs to be solved. There have been related studies focusing on API compatibility issues of Python third-party libraries, of which reasons have yet to be fully classified so that, the fine-grained cause can not be provided. An empirical study is conducted on the symptoms and causes of API compatibility issues with Python third-party library and a targeted static detection method is proposed. Initially, this study gathers 108 pairs of incompatible API versions by combining version update logs and regression tests across 6 version pairs of the Flask and Pandas libraries. Subsequently, an empirical study is conducted on the collected data, summarizing the symptoms and causes of compatibility issues. Finally, this study proposes a static analysis-based detection method for incompatible Python APIs, providing syntactic-level causes of incompatible API issues. This study conducts experimental evaluations on 12 version pairs of 4 popular Python third-party libraries. The results show that the proposed method is good in effectiveness, generalization, time performance, memory performance, and usefulness.