Drift current in PN Junction
By the definition of the drift current we can understand that this current is made from minority carriers, so it is made between the holes in the N region and the free electrons in the P region (The minority carriers)


Both majority and minority carriers can participate in drift current, not just minority carriers. However, pn junction diodes are considered a "minority carrier device" due to the current control coming from the diffusion of minority carriers.

Drift current occurs whenever there an some electric field that causes the carriers to exhibit a net flow. There is no reason an electric field would effect just the minority carriers.


  but how can the drift current flow if the free electrons in the P region are pushed away from negative zone of the depletion zone that attract holes, and the holes in N zone are pushed away from the positive zone of the depletion region (That will attract free electrons), 


Exactly what you describe is what causes the drift current. I'm unclear about why you think it doesn't.

The electric fields created in the depletion region by the ionized dopants are what create the electric field leading to the drift current. A free electron in the depletion region will be forced toward the N side of the junction (right in your picture) and a hole will be forced toward the P side of the junction (left in your picture).

A diode in equilibrium is a balance of drift and diffusion currents that at equilibrium exactly cancel each other out.