Droplet coalescence has received significant attention due to its significant role in fluid mixing, microfluidics, coalescence-induced droplet jumping, and heat and mass transfer applications. Coalescence of droplets has been extensively investigated from the perspectives of hydrodynamics and energy transfer. However, the study of coalescence characteristics of size-mismatched droplets on superhydrophobic surfaces remains a challenge due to visualization difficulty, limited droplet size control, and poor droplet manipulation. Here, in order to study coalescence dynamics of droplets with arbitrary initial sizes, a droplet dispensing and visualization system was developed. To control the size of droplets, monodispersed droplets with radii of ≈20 μm were dispensed using a frequency-controlled piezoelectric pulse injector onto a superhydrophobic surface, enabling the target droplets to accumulate in volume and grow in radii. The coalescence process of droplets having radii of ≈270 and ≈780 μm was imaged at a magnification of ≈25X and capture rate of 13000 fps. Surprisingly instead of completely merging together, the size-mismatched droplets underwent partial coalescence with the development of an additional satellite droplet. Specifically, the smaller droplet gave 'birth' to a secondary satellite droplet upon coalescence with the larger primary droplet due to liquid-bridge pinch-off dynamics, after which the satellite droplet bounced off upon collision with the primary droplet due to the presence of an air cushion that blocked contact between the two droplets. Meanwhile, the primary droplet continued to oscillate while the bouncing satellite droplet returned to the surface and eventually bounced off (moving direction is identified with arrows). Our work not only presents a powerful platform capable of both controlling and visualizing droplet coalescence hydrodynamics, but also provides insights into the flow hydrodynamics of droplets undergoing partial coalescence.