Adaptive radiotherapy (ART) enhances prostate cancer treatment by accounting for daily anatomical variations, but clinical implementation remains limited due to the need for accurate and efficient auto segmentation; manual corrections after automated contouring often hinder workflow efficiency. To address this, we propose a patient-specific network (PSN) approach for clinical target volume (CTV) segmentation using cone-beam computed tomography (CBCT). This retrospective study included 26 prostate cancer patients treated with CBCT-guided online ART using the Ethos therapy system, comprising 119 retrospectively exported fractions. The PSN framework uses a two-stage strategy: initial pre-training followed by patient-specific fine-tuning via PSNadaptive or PSNsequence, implemented with the Swin UNETR architecture. This approach is distinct from static personalization methods as it continuously adapts to daily anatomical changes. Segmentation performance was compared against deformable registration and generalized deep learning models using the Dice similarity coefficient (DSC), 95th percentile Hausdorff distance (HD), and mean surface distance (MSD). PSN significantly improved segmentation performance, with PSNadaptive achieving a DSC of 0.978 ± 0.005, HD of 1.681 ± 0.743 mm, and MSD of 0.510 ± 0.035 mm by the fifth fraction, with accuracy improving across sequential fractions. Visual assessments confirmed high agreement with physician contours, especially in anatomically complex regions. These findings support the PSN framework as a clinically feasible and accurate solution for patient-specific segmentation in prostate ART, potentially reducing the need for manual editing, streamlining workflow efficiency, and enhancing the precision of adaptive treatment delivery.