Millimeter-wave (mmWave) and sub-Terahertz (THz) frequencies are expected to play a vital role in 6G wireless systems and beyond due to the vast available bandwidth of many tens of GHz. This paper presents an indoor 3-D spatial statistical channel model for mmWave and sub-THz frequencies based on extensive radio propagation measurements at 28 and 140 GHz conducted in an indoor office environment from 2014 to 2020. Omnidirectional and directional path loss models and channel statistics such as the number of time clusters, cluster delays, and cluster powers were derived from over 15,000 measured power delay profiles. The resulting channel statistics show that the number of time clusters follows a Poisson distribution and the number of subpaths within each cluster follows a composite exponential distribution for both LOS and NLOS environments at 28 and 140 GHz. This paper proposes a unified indoor statistical channel model for mmWave and sub-Terahertz frequencies following the mathematical framework of the previous outdoor NYUSIM channel models. A corresponding indoor channel simulator is developed, which can recreate 3-D omnidirectional, directional, and multiple input multiple output (MIMO) channels for arbitrary mmWave and sub-THz carrier frequency up to 150 GHz, signal bandwidth, and antenna beamwidth. The presented statistical channel model and simulator will guide future air-interface, beamforming, and transceiver designs for 6G and beyond.