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The Galactic Center ridge has been observed extensively in the past by both GeV and TeV gamma-ray instruments revealing a wealth of structure, including a diffuse component and the point sources G0.9+0.1 (a composite supernova remnant) and Sgr A* (believed to be associated with the supermassive black hole located at the center of our Galaxy). Previous very high energy (VHE) gamma-ray observations with the H.E.S.S.. experiment have also detected an extended TeV gamma-ray component along the Galactic plane in the >300 GeV gamma-ray regime. Here we report on observations of the Galactic Center ridge from 2010 to 2014 by the VERITAS telescope array in the >2 TeV energy range. From these observations we (1) provide improved measurements of the differential energy spectrum for Sgr A* in the >2 TeV gamma-ray regime, (2) provide a detection in the >2 TeV gamma-ray emission from the composite SNR G0.9+0.1 and an improved determination of its multi-TeV gamma-ray energy spectrum, and. (3) report on the detection of VER J1746-289, a localized enhancement of >2 TeV gamma-ray emission along the Galactic plane.