Organic materials with tunable chemical and mechanical properties are ideal for interfacing with skin and tissue in biomedical applications. While polymer semiconductors (PSCs) have advanced toward skin-like mechanical performance, the limited capacity for biofunctionalization has restricted their biosensing applications. In this study, we introduce a direct biofunctionalization strategy for PSCs based on thiol-ene chemistry. We selectively grafted thiolated biomolecules (e.g., aptamers) onto elastomeric domains within an interconnected semiconductor/elastomer network. This approach enables high-resolution patterning down to 10 micrometers while preserving the electronic performance of PSCs. Leveraging this platform, we designed and fabricated skin-like electrolyte-gated organic field-effect transistors with biofunctionalized channels. These soft and stretchable devices exhibit stable operation in physiological buffers for more than 50 days and maintain performance under up to 50% strain. When functionalized with cortisol-binding aptamers, the sensors achieved sensitive detection across physiologically relevant concentrations, down to the picomolar range. This work establishes a foundation for integrating stretchable and biofunctional PSCs into skin-like wearable devices.