If we have electric field and we put electron there , the electron will move in the opposite direction as the electric field. My question is electron in that direction will speed up or slows down ? And what happens to Electric potential energy of that electron, it will increase or decrease?
I can see how easy it is to be missunderstood!
Your question is a valid one, at least from physics point of view.
Here is how you can think about it:
Imagine you put an electron inside a uniform electric field, like the electric field between two metallic plates for example. At that position the electron will experience a force which will be towards the plate with the positive sign. The electron will be accelerated in that direction and its kinetic energy will increase, but that will be in the expence of the elictrical potential energy of the electron which will decrease by the same amount. So the total energy of the electron is fixed. This reflects the principle of energy conservation. You can write an equation that gives you a good picture of what happens to the various energies of the electron
where $v_1$, is speed of the electron at the point where you place it inside the electric field, and $V_1$ is its electrical potential energy at that point. Similarly for $v_2$ and $V_2$, are the speed and potential energy at some point closer to the positive metallic plate.
You can see from this equation that as KE increases, the electrical potential energy decreases. The total energy remains fixed!
I hope this helps you a bit to understand what happens to the energy.