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This letter introduces a new class of miniaturized reflectarray unit cells with increased phase swing employing Minkowski fractal-shaped patch-slot elements. Square, 1st Minkowski, and 2nd Minkowski fractal patches are designed as a reflectarray unit cell. A slot with variable lengths of 0 <; Ls <; 6 mm is used in the ground plane to perform the phase variation function. The resonant frequency corresponding to the maximum phase swing is reduced from 10.6 GHz for the square patch down to 8.8 and 8.3 GHz for the first- and second-order Minkowski fractal patches, respectively, which is equivalent to 17% and 22% size reduction. Unit cells with different patch type and slot length are fabricated, and close agreement is observed between the measured and simulated results. As it has been proven for conventional phased array antennas, this size reduction can lead to a decrease in mutual coupling in reflectarray antennas. Alternatively, it allows for smaller distance between reflectarray antenna elements, which renders a wider beam-scanning range.