We report a terahertz quantum-cascade vertical-external-cavity surface-emitting laser (QC-VECSEL) based upon a metasurface consisting of an array of gain-loaded resonant patch antennas. Compared with the typical ridge-based metasurfaces previously used for QC-VECSELs, the patch antenna surface can be designed with a much sparser fill factor of gain material, which allows for reduced heat dissipation and improved thermal performance. It also exhibits larger amplification thanks to enhanced interaction between the incident radiation and the QC-gain material. We demonstrate devices that produce several milliwatts of continuous-wave power in a single mode at ~4.6 THz, and dissipate less than 1 W of pump power. Use of different output couplers demonstrates the ability to optimize device performance for either high power, or high operating temperature. Maximum demonstrated power is 6.7 mW at 4 K (0.67% wall-plug efficiency (WPE)), and 0.8 mW at 77 K (0.06% WPE). Directive output beams are measured throughout with divergence angles of ~5°. THE MANUSCRIPT The terahertz (THz) quantum-cascade (QC) vertical-external-cavity surface-emitting laser (VECSEL) is a recently developed approach for designing THz QC-lasers with scalable output power and high-quality beam patterns. 1 The enabling component of the QC-VECSEL is an amplifying metasurfacea reflectarray of resonant antenna-coupled THz QC-gain elements with subwavelength spacing that exhibits a reflectance R greater than unity across some finite gain bandwidth. The antenna elements are unable to lase on their own due to high surface radiation losses, but instead, the metasurface is used as the amplifying element of an external cavity laser. The external cavity mode effectively phase locks the antenna elements, and because the metasurface can be made large relative to the lasing wavelength, near-diffraction-limited beams with high power have been observed. 2 The external-cavity allows one to more easily modify the outcoupling efficiency and cavity resonant frequency, 3 while the metasurface offers unique opportunities such as engineering of "flat-optics" focusing 2 and polarization switchability. 4 The typical metasurface design consists of a 1D sub-wavelength array of narrow metal-metal ridges of width w and period Λ that are coupled to surface radiation via the TM01 cutoff resonances of the ridges. 5,6 This design has been used to realize many high-performance VECSELs operating between 3-4 THz. 3,7,8