This Letter demonstrates a novel, to the best of knowledge, overlapping single-sideband (OSSB) transmission scheme for spectrally efficient multi-service fiber-wireless (FiWi) access in a low-cost direct-detection (DD) THz system. Utilizing the proposed OSSB scheme, user data from different services can share the same spectrum resource yet can be successfully demodulated via one cost-effective DD THz receiver in conjunction with the Kramers-Kronig (KK) based SSB field reconstruction and look-up table (LUT) enabled signal separation algorithms. A proof-of-principle experiment is conducted. Based on an IQ modulator and a single THz zero-bias diode (ZBD), two independent 10-GBd quadrature phase shift keying (QPSK) signals with an overlapped spectrum are successfully demodulated after 20-km fiber and up to 3-m wireless transmission at the 300-GHz band. To the best of our knowledge, this is the first demonstration of multi-service FiWi access with an OSSB format in a 300-GHz DD THz system.