Non-invasive prenatal testing (NIPT) enables accurate detection of fetal chromosomal trisomies. The majority of publicly available computational methods for sequencing-based NIPT analyses rely on low-coverage whole-genome sequencing (WGS) data and are not applicable for targeted high-coverage sequencing data from cell-free DNA samples. Here, we present a novel computational framework for a targeted high-coverage sequencing-based NIPT analysis. The developed framework uses a hidden Markov model (HMM) in conjunction with a supplemental machine learning model, such as decision tree (DT) or support vector machine (SVM), to detect fetal trisomy and parental origin of additional fetal chromosomes. These models were developed using simulated datasets covering a wide range of biologically relevant scenarios with various chromosomal quantities, parental origins of extra chromosomes, fetal DNA fractions, and sequencing read depths. Developed models were tested on simulated and experimental targeted sequencing datasets. Consequently, we determined the functional feasibility and limitations of each proposed approach and demonstrated that read count-based HMM achieved the best overall classification accuracy of 0.89 for detecting fetal euploidies and trisomies on simulated dataset. Furthermore, we show that by using the DT and SVM on the HMM classification results, it was possible to increase the final trisomy classification accuracy to 0.98 and 0.99, respectively. We demonstrate that read count and allelic ratio-based models can achieve a high accuracy (up to 0.98) for detecting fetal trisomy even if the fetal fraction is as low as 2%. Currently, existing commercial NIPT analysis requires at least 4% of fetal fraction, which can be possibly a challenge in case of early gestational age (<10 weeks) or high maternal body mass index (>35 kg/m2). More accurate detection can be achieved at higher sequencing depth using HMM in conjunction with supplemental models, which significantly improve the trisomy detection especially in borderline scenarios (e.g., very low fetal fraction) and enables to perform NIPT even earlier than 10 weeks of pregnancy.