We report a compact single-cell source of a continuous cold-atom beam with three-dimensional (3D) cooling. By integrating an off-axis moving optical molasses (OM) with a two-dimensional magneto-optical trap, we achieve simultaneous 3D cooling within a $50\mathrm{mm}$ interaction region. The source delivers a continuous flux up to $4.9(5)\times {10}^9\mathrm{atoms}/\mathrm{s}$, with a transverse temperature of $94(5)\text{μ}\mathrm{K}$, a longitudinal temperature as low as $231(65)\text{μ}\mathrm{K}$, and a tunable mean velocity between 5 and $20\mathrm{m}/\mathrm{s}$. Custom in-vacuum mirrors integrate the reflective geometry for the off-axis OM beams with a $0.8\mathrm{mm}$ output aperture, ensuring stable alignment while suppressing stray light and fluorescence leakage. Ultralow light shift and decoherence are verified via continuous Raman-Ramsey interferometry, yielding a light shift of $-0.51(4)\mathrm{Hz}$ and a typical fringe contrast of $90.85(30)\mathrm{\%}$ at a Raman separation of $100\mathrm{mm}$ (interrogation time of $8.70\mathrm{ms}$). This compact continuous cold-atom beam source constitutes a practical building block for atomic-beam clocks and interferometers, enabling reduced aliasing noise together with improved sensitivity and accuracy for field applications.

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• Atom interferometry
• Atomic & molecular processes in external fields
• Atomic, optical & lattice clocks
• Cooling & trapping
• Spontaneous emission
• Stark effect
• Atomic & molecular beams
• Devices