We present a reversible biosignal steganography method to authenticate the source of biosignal in this paper. Cloud is being a popular platform for storing a large volume of biosignals such as an electrocardiogram (ECG), electroencephalogram (EEG), and photoplethysmogram (PPG). However, outsourcing biosignals to the cloud may introduce authenticity issues. For instance, patient data can be altered, or fake patient data can be inserted by the dishonest cloud service provider or attacker for giving benefits to business organizations such as insurance service providers. Steganography approaches can be used to hide data source's identification data before outsourcing to the cloud for maintaining authenticity. Existing biosignal steganography approaches fail to reconstruct original biosignal after applying a reverse data hiding technique. In other words, current biosignal steganography approaches are irreversible. Reversible biosignal steganography method is required for protecting biosignal data from deterioration and efficient use by its stakeholders. In this work, we develop a reversible biosignal steganography approach using the Extended Binary Golay Code based error correction method. Our proposed method embeds secret authentication message as an error within different types of biosignals such as ECG, PPG, and EEG. Extended Binary Golay Code based error correction method is used to extract the secret message, and reconstruct original biosignal. We conduct a set of experiments for evaluating the performance of our proposed method.