What happens to the energy of photon red shifted by expansion of universe? There are many similar questions but the answers don't satisfy me.
I mean it as asked in the title. Some answers given before give the explanation based on gravitational potential energy but consider one generates photon in open space with something small like bulbs photon will still face red shift but have not to overcome any gravity. I mean only by expansion of universe. In what way energy of it will decrease.
The second thing is the expansion of the universe is an accelerated process so energy will continue to drain from photon and it should be in a continuous fashion but energy is quantized. photon wavelength is not quantized but i am talking about energy that is lost if we are considering that energy is being lost gets into space-time or anywhere else, lost energy should be quantised but as expansion is accelerative continuous energy loss appear to occur free particles have continuous energy but it have to be associated with photon all the time.
I understand that energy not considered as conserved in cosmology but based on that argument can we say the energy of photon is reduced and we have no need to give any explanation to it, just like that.
 A: 
I understand that energy not considered as conserved in cosmology but based on that argument can we say the energy of photon is reduced and we have no need to give any explanation to it, just like that.

It's not true that energy is not conserved in cosmology. Energy is locally conserved but not globally conserved.

The second thing is the expansion of the universe is an accelerated process so energy will continue to drain from photon and it should be in a continuous fashion but energy is quantized.

The energy of free particles is not quantized, it's continuous.

Some answers given before give the explanation based on gravitational potential energy

It's impossible to reply in detail because you haven't linked to the answers. However, this is wrong. There is no notion of gravitational potential energy that applies to cosmological spacetimes.
shai horowitz says in a comment:

The energy could be considered going into slightly slowing the rate of expansion of the universe.

No, this is wrong. This assumes that there is a globally conserved energy that needs to be conserved, which is not the case.
