We present a technique for generation of tripartite quantum-correlated amplitude-squeezed light beams, using frequency doubling in a singly resonant cavity with two output ports. The two-output second-harmonic (SH) beams are both nonlinearly coupled to the common fundamental beam even though they have no direct interaction. The nonlinear coupling produces noise reduction of amplitude for each beam and quantum correlations among three beams. In our first experiment, we measured amplitude squeezing of 0.5, 0.8, and 0.6 dB for the fundamental beam and two output SH beams, respectively. Meanwhile, quantum correlation of 0.6 dB between the two amplitude-squeezed SH beams and quantum anticorrelation of 0.6 and 0.8 dB between the squeezed fundamental beam and each of the SH beams were observed around the range of optimum conversion efficiency. This opens an alternate way to produce tripartite-quantum-correlated systems.