Developing an intelligent technique for fetal heartbeat detection to monitor the cardiac function of the fetus in the initial stages of pregnancy is crucial. In this research work, two hybrid algorithms are proposed that use a combination of recursive least square algorithm (RLS) and stationary wavelet transform (SWT) for fetal ECG extraction. The goal of this research is to enhance the fetal ECG signal, reduce noise and artifact, and accurately detect the R-peaks by employing improved spatially selective noise filtration (ISSNF) method or threshold-based denoising approach in the wavelet domain. Accurate fetal R-peak detection can provide important clinical information and aid in the diagnosis and treatment of fetal heart conditions. The primary aim is to extract a clear fetal ECG signal from the mixed abdominal signal. The abdominal signal is divided into multiscale components using SWT, with different levels of noise determining the scale of wavelet decomposition. The RLS algorithm is then utilized for removing maternal ECG components, and either ISSNF or threshold-based algorithms are employed for denoising in the wavelet domain. We evaluate the effectiveness of our proposed method using both synthetic and clinical data. Our analysis involves qualitative and quantitative measures, including visual inspection, signal-to-noise ratio (SNR) computation, and QRS complex recognition. Our findings reveal that the proposed system exhibits superior performance when compared to conventional adaptive filtering techniques. The experimental results suggest that the proposed system has the potential to extract fetal ECG signals that are clear, with good SNR results and minimal disturbances.