Is nuclear force a field force or not? I mean, whatever the source of the force is, does it create a field around it just like a body with mass and a body with charge do.
If yes,then can we use the concepts of potential energy to explain microscopic phenomena in an atom? 
 A: There are two things referred to in the Standard Model, the strong force (which I guess is what you are referring to) and the weak force. The latter is just a way to describe particle decay. In quantum field theory, they are both fields. When we use the term ‘‘force’’ we mainly use the force effect of the field.
In retrospect, both forces contribute to atomic phenomenon, in which case they are referred to as the strong nuclear force and the weak nuclear force. The strong nuclear force is an attractive force between protons and neutrons that keep the nucleus together and the weak nuclear force is responsible for the radioactive decay of certain nuclei.
The source of the strong force is any particle carrying what we call a color charge. The color charge is analogous to the electric charge for the electromagnetic field or the mass for the gravitational force.
The strong field does, of course, have a potential energy. The strong nuclear field is observable at two ranges inside the atom: on a larger scale (about 1 to 3 fm), it is the force that binds protons and neutrons together to form the nucleus of an atom. On the smaller scale (less than about 0.8 fm, the radius of a nucleon), it is the force that holds quarks together to form protons, neutrons, and other hadron particles.
A: 
I mean, whatever the source of the force is,

The nuclear force is a spillover force from the strong interactions that go on continually among the quarks and gluons in the nucleus. This is an illustration of the proton
 
which although color neutral , as also all hadrons, spill over forces can escape and interact with other hadrons, similar to the van der Waals forces between atoms and molecules which allow variations of postive and negative fields which hold the atoms and molecules into solids and liquids.

does it create a field around it just like a body with mass and a body with charge do.

see above

If yes,then can we use the concepts of potential energy to explain microscopic phenomena in an atom? 

Not atoms, atoms are explained by electromagnetic forces, not the strong nuclear force. The strong nuclear force explains the periodic table of elements and there are various models, for example the shell model for nuclei  a phenomenological  potential  well model.
