We study the effective $s$-wave scattering of two heteronuclear atoms harmonically confined in quasi-low dimensions, where the atoms have unequal masses and are subject to different confinement frequencies. The resulting effective scattering parameters in low dimensions, including scattering length and effective range, are derived as functions of three-dimensional scattering parameters and confinement strengths. Using realistic Li-K and Li-Cr mixtures as examples, we further compute the binding energies of universal $(1+N)$ clusters in quasi-low dimensions using the effective scattering parameters. Our findings suggest a promising pathway for practically observing universal clusters and their associated many-body phases in low-dimensional ultracold heteronuclear systems.

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• Scattering of atoms, molecules, clusters & ions
• Atomic gases
• Confinement-induced resonance