Photons are the quantum elementary particles of the electromagnetic force . In the table there are elementary particles with charge other than electrons so photons can be produced at the basic level by other charged particles too.

One way they are produced in the way you have been taught at present, by changes in the energy level in atoms, which are composed of electrons and a positively charged nucleus.

Another way is by the scattering of charged particles off the field of other charged particles. This classically is described by the production of light from accelerating charged particles. Classical electricity and magnetism can be shown to emerge from the underlying quantum mechanical level.

how will the electromagnetic force will come between two individual protons? Is there more ways to generate photons?

Individual protons are composite charged particles and may generated photons when scattering off each other's electromagnetic field. The Coulomb force between two protons can be shown in quantum field theory to derive from the mathematical existence of virtual photons , but this needs graduate studies in quantum field theory to understand.

Photons are the quantum elementary particles of the electromagnetic force . In the table there are elementary particles with charge other than electrons so photons can be produced at the basic level by other charged particles too.

One way they are produced is the way you have been taught at present, by changes in the energy level in atoms, which are composed of electrons and a positively charged nucleus.

Another way is by the scattering of charged particles off the field of other charged particles. This classically is described by the production of light from accelerating charged particles. Classical electricity and magnetism can be shown to emerge from the underlying quantum mechanical level.

how will the electromagnetic force will come between two individual protons? Is there more ways to generate photons?

Individual protons are composite charged particles and may generate photons when scattering off each other's electromagnetic field. The Coulomb force between two protons can be shown in quantum field theory to derive from the mathematical existence of virtual photons , but this needs graduate studies in quantum field theory to understand.