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Context. RACE-OC (Rotation and ACtivity Evolution in Open Clusters) is a project aimed at characterising the rotational and magnetic activity properties of the late-type members of open clusters, stellar associations, and moving groups of different ages. The evolution in time of rotation and activity at different masses sheds light on the evolution of the stellar internal structure, on magneto-hydrodynamic processes operating in the stellar interior, and on the coupling and decoupling mechanisms between the radiative core and the external convective envelope. As part of this project, in the present paper we present the results of an investigation of a likely member of the AB Doradus association, the M-type star 2MASS J15594729+4403595. Aims. In the present study, we aim to reveal the real nature of our target, which turned out to be a hierarchical triple system, to derive the stellar rotation period and surface differential rotation, and to characterise its photospheric magnetic activity. Methods. We have collected radial velocity and photometric time series, complemented with archive data, to determine the orbital parameters and the rotation period and we have used the spot modelling technique to explore what causes its photometric variability. Results. We found 2MASS J15594729+4403595 to be a hierarchical triple system consisting of a dwarf, SB1 M2, and a companion, M8. The M2 star has a rotation period of P = 0.37 d, making it the fastest among M-type members of AB Dor. The most relevant result is the detection of a periodic variation in the spotted area on opposite stellar hemispheres, which resembles a sort of Rossby wave or Rieger-like cycles on an extremely short timescale. Another interesting result is the occurrence of a highly significant photometric periodicity, P = 0.443 d, which may be related to the stellar rotation in terms of either a Rossby wave or surface differential rotation. Conclusions. 2MASS J15594729+4403595 may be the prototype of a new class of extremely fast rotating stars exibiting short Rieger-like cycles. We shall further explore what may drive these short-duration cycles and we shall also search for similar stars to allow for a statistical analysis.