This paper presents a novel robotic finger prosthesis for partially amputated patients who have lost a thumb and index finger. The challenging issues were to design i) a three-degree-of-freedom (DOF) underactuated mechanism that mimics intact finger movements including motion profiles and self-adaptation for unknown constraints, ii) an attachment socket for everyday life that allows ease of donning and doffing, and comfortable wearability, and iii) a shape to pack the selected components including an actuator, linkages, and sensors into a limited space avoiding motion interference with other intact fingers and wrist. This paper reports our effort to solve the challenging issues. The proposed three-DOF prosthetic finger can generate 4.6N pinch force and 99.4°/s angular velocity at the MCP joints. For command signals, surface-electromyogram (sEMG) sensors were used. This enables users to operate the fingers with certain configuration and grasping force. The performance of the proposed design was verified through the box-and-block test and bottle opening test with a patient who has a partially amputated hand.