The effect of Co-doping on the structure, microstructure, martensitic phase transformation kinetics, and magnetic properties of the melt-spun (Ni50Mn40In10)1−xCox (x = 1, 2, and 3) Heusler ribbons, named hereafter Co1 (x = 1), Co2 (x = 2), and Co3 (x = 3), was assessed using X-ray diffraction, scanning electron microscope, energy-dispersive spectroscopy, X-ray fluorescence, differential scanning calorimetry, and vibrating sample magnetometer. The XRD results reveal the formation of a 14M martensite structure alongside the face-centered-cubic (fcc) γ phase. The crystallite size ranges between 50 and 98 nm for the 14M martensite and from 9 to 16 nm for the γ phase. The mass fraction of the γ phase lies between 36.4 and 44.2%. Co-doping affects the lattice parameters and the characteristic temperatures (martensite start, martensite finish, austenite start, and austenite finish). The calculated activation energy values for the non-isothermal martensitic transformation kinetics are 257 kJ mol−1 and 135.6 kJ mol−1 for the Co1 and Co2, respectively. The produced ribbons show a paramagnetic behavior. The variation in the coercivity can be related to the crystallite size and mass fraction of the γ phase. The produced ribbons exhibit an exchange bias at room temperature that decreases with increasing the Co content.