Circulating tumor DNA (ctDNA) provides a minimally invasive molecular signal for cancer detection, residual disease assessment, treatment-response monitoring, and recurrence surveillance; however, reliable identification becomes difficult when tumor-derived fragments occur at very low variant allele fractions within a dominant background of normal cell-free DNA. This study develops OncoSignal, a novel computational algorithm for detecting low-abundance ctDNA through integrated background-error modelling, fragment-level signal weighting, molecular-context encoding, adaptive denoising, probabilistic evidence fusion, and confidence-calibrated classification. Unlike conventional fixed-threshold approaches that classify candidate variants primarily according to read depth, allele frequency, or predefined quality cut-offs, OncoSignal constructs a multidimensional evidence score from variant allele frequency, base quality, mapping quality, strand consistency, fragment length, genomic context, local sequencing error, molecular support, and locus-specific noise characteristics. The proposed architecture incorporates an Adaptive Molecular Noise Suppression module, Fragment-Context Attention Network, Bayesian Evidence Fusion layer, and Dynamic Signal Decision Boundary, allowing the detection threshold to adjust to sequencing depth, background error distribution, and sample-specific noise. OncoSignal is designed for comparative benchmarking against conventional variant allele frequency thresholding, statistical binomial detection, logistic regression, support vector machine, random forest, XGBoost, multilayer perceptron, one-dimensional convolutional neural networks, long short-term memory networks, and Transformer-based classifiers. Performance is evaluated across progressively decreasing ctDNA fractions using sensitivity, specificity, precision, F1-score, Matthews correlation coefficient, area under the receiver operating characteristic curve, area under the precision-recall curve, false-positive rate, calibration error, signal-to-noise ratio, and limit of detection. Particular emphasis is placed on the clinically demanding low-abundance interval below 1% variant allele frequency and the ultra-low range below 0.1%. Comparative graphical analysis includes ROC and precision-recall curves, sensitivity-versus-variant-allele-frequency profiles, three-dimensional surfaces relating sequencing depth, tumor fraction, and detection probability, calibration plots, signal-to-noise distributions, and error-rate comparisons across algorithms. The central hypothesis is that adaptive integration of molecular evidence and locus-specific background modelling will preserve true weak tumor signals while suppressing sequencing artefacts more effectively than fixed thresholds and conventional machine-learning classifiers. The resulting OncoSignal framework is intended to provide a more sensitive, specific, interpretable, and technically robust computational platform for low-abundance ctDNA detection and subsequent liquid-biopsy applications.