Why the inlet of an air compressor pushes away my hand? 
This is a picture of an air compressor. It compresses air up to 30 bar. The black part on the top of it is the air inlet.
When I place my hand exactly at the air inlet, of course it tends to draw my hand inside.
But when I place my hand a little bit further, against my intuition  it pushes my hand outside. 
Does anybody has any description about this phenomenon?
 A: This phenomenon is the Coanda effect. Coandă effect made the air compression and conditioning possible in form of products. This effect along with Bernoulli Principle can also be observed in flight of airplanes.
In the case of harmattan compressor that you've shown in picture, as the air is being compressed and forced out of the inlet, it flows past the surface of your hand and is being attracted to it.
When you hold your hand closer to the inlet, you feel a small concentrated suction of high speed air and is able to pull your hand towards the inlet.
When your hand is further away from the inlet, the air has expanded and its velocity has decreased, so it is less able to create a strong enough force to pull your hand towards the inlet. Instead, the air is flowing over the surface of your hand and creating a pressure difference between the front and the back of your hand, resulting in your hand being pushed away from the inlet. This pressure difference is known as the Bernoulli's principle
In short, when your hand is closer to inlet, it is creating low pressure in front of your hand and when your hand is away from inlet, it is creating a low pressure on back of your hand because the air has sxpanded and will try to suck air from back of your hand
The following picture can partially explain it. It is "up/down pressure" version of your scenario (back/front of hand)

A good video explaination
https://www.youtube.com/watch?v=21YB4qCvIK4
Another quite useful and relevant observation is in magnus effect. In following gif from wikipedia. Just replace the spinning movement with air compression. Instead spinning ball altering the pressure to move, we can suppose the fluid/air creating a low pressure on back of ball causing it to push away.
https://upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Magnus_effect.gif/220px-Magnus_effect.gif
A: It is not uncommon for an air compressor to emit a small backwards puff of air out the inlet while running, depending on the check valve design that is supposed to open freely when the compressor pulls in a charge of ambient air and then close tightly shut when the machine begins to compress that charge.
If the check valve has only a small amount of preload urging it normally closed, then part of the charge being compressed will naturally "blow back" in the process of closing the check valve, and the inlet flow will run backwards for a brief moment.
If you put your hand over the inlet to completely occlude it, then the compressor begins to act as a vacuum pump and its inlet plenum (that portion of the plumbing between the check valve and your hand) will pull down to subatmospheric pressure and the check valve will stop cycling open and shut because there are no forces acting on it to open and shut- so, no puffs.
I suggest you light a candle near the inlet while the pump is running and blow out the flame, so the pump will ingest some smoke. If you are skilled and lucky, then you might be able to see the backwards puff in action. a short tuft of knitting yarn held near the inlet may also reveal the back puff- but whatever you do, DO NOT LOSE YOUR GRIP ON THE TUFT because the pump will not like it if it gets sucked into the works!
