The photon goes at the speed of light in a vacuum or water,
The photon is an elementary particle with mass zero. All zero mass elementary particles travel in vacuum with the velocity of classical electromagnentic waves,light , c, because of the Lorenz covariance of the quantum field theory. Light is an emergent phenomenon from a large number of photons, as can be seen experimentally here.
but not its wave which goes at a speed C / n,
The photon as an elementary quantum particle has a wave function, but the wave dependence for the photon is in the probability distribution for detecting it (as in the single photon experiment linked above), not in space. The emergent classical electromagnetic wave, light, from the same energy photons displays an energy distribution as a function of space coordinates.
and if the electron goes at the same speed as the wave of light in the water
If the electron goes at the speed or more of light in water, it emits cerenkov radiation as explained in the answer of Toby.
in the same space-time,
Two elementary particles, as a photon and an electron, in the same space time interact and the probability of interaction is calculable in quantum electrodynamics, so this you describe cannot happen:
the two quantum probability equations will give rise to a single equation.
The photon beam and the electron beam, to be beams, will always be governed by two independent quantum probability equations
And in this quantum equation the quantum overlap will allow the electron to go faster than C and photon to go slower than C.
The photon always goes at c. It is the emergent classical wave that can have velocity lower than c in a medium. The classical wave is a state defined by quantum mechanics in a complicated way, as the superposition of photons, and needs quantum field theory to be understood, see here.