Is Gravitational Red shift equal to $mgh$ Is gravitational shift - $\frac{gh}{c^2}$  (according to pound-rebka experiment) always equal to $PE=mgh$? because assume the gravitational pull, $g$, is equal to $1$ then we can say $g = 1$ similarly let us assume the height the photon wants to travel is also $1$ therefore $h=1$ and now let us assume the mass is $1$ so $m = 1kg$ now that we know if we plug in this into the following equations we get an imbalance as:
$$\frac{gh}{c^2} = \frac{1}{c^2} = 1.11265006 * 10^{-17} J\approx Negligible$$ 
Now lets assume we convert this energy into mass again using $E=mc^2$ where $m = E/c^2$ which is $1kg$ with some 
while if we now plug in the values into the potential energy we get: $$PE = mgh = 1*1*1 = 1J$$
and we know $1 > (1.11265006 * 10^{-17})$
and since we know that potential energy is always equal to kinetic energy we can say that Gravitational Redshift creates an energy imbalance which goes against laws of Thermodynamics so what makes sure that gravitational redshift becomes equal to $mgh$?
 A: Always include units
Always. No exception. Ever. If your Nobel prize winning professor writes down equations like this without units, you look him in the eye and tell him he's not doing physics.
Your analysis suffers from the fatal flaw that you are comparing quantities with different units. $gh/c^2$ is dimensionless. It is the fractional energy change in a photon over a short distance where $g$ can be taken to be constant.
On the other hand, $mgh$ is the absolute change in potential energy over a similarly short distance. It has units of energy.
Moreover, $mgh$ doesn't apply to massless particles like photons anyway. Classical physics doesn't deal with relativistic things very well, since otherwise we would have predicted gravitational redshift centuries before general relativity.
You might see some things work out better if you scale to the same dimensions. If $mgh$ is the absolute change in energy, then the fractional change in energy should be $mgh/E$. If you just blindly apply $E = mc^2$, you retrieve $gh/c^2$. Be warned, though, that such carefree application of a cliche equation like this isn't always a good idea. If you ever find yourself talking about the mass of a massless particle, you should immediately start backtracking and looking for any suspect steps you took, rather than just forging ahead by throwing more equations at the problem.
