Let’s consider a very distant galaxy, suppose it has no peculiar velocity, and let’s assume space expansion; If I understand correctly there would be a redshift due to the value of space expansion at the time when photons were emitted from this galaxy, then there would be a redshift due to space expansion (and its possible variations) all along the travel in space and time of these photons toward our present point of observation. How do these two redshift values compare? Is the first one negligible compared to the second one?
Here is what redshifts we are talking about:
The light from most objects in the Universe is redshifted as seen from the Earth. Only a few objects, mainly local objects like planets and some nearby stars, are blueshifted. This is because our Universe is expanding. The redshift of an object can be measured by examining the absorption or emission lines in its spectrum. These sets of lines are unique for each atomic element and always have the same spacing. When an object in space moves toward or away from us, the absorption or emission lines will be found at different wavelengths than where they would be if the object was not moving (relative to us).
The unshifted is what the particlular atomic spectrum looks in our laboratories here on earth. The red shifted tell us that the light comes from original atoms that are receeding from us, and the blue shifted tell us that the atoms are approaching us, with the corresponding velocity
Continuing from the link:
The cosmological redshift is a redshift caused by the expansion of space. As a result of the Big Bang (the tremendous explosion which marked the beginning of our Universe), the Universe is expanding and most of the galaxies within it are moving away from each other. Astronomers have discovered that all distant galaxies are moving away from us and that the farther away they are, the faster they are moving. This recession of galaxies away from us causes the light from these galaxies to be redshifted. As a result of this, at very large redshifts, much of the ultraviolet and visible light from distant sources is shifted into the infrared part of the spectrum. This means that infrared studies can give us much information about the ultraviolet and visible spectra of very young, distant galaxies.
With this in mind, the spectra from receding galaxies have all the information about the expansion of space too. It is the velocities of the original source that are recorded in the spectra, whether due to orbital motions or space expansion, at the source the velocities are added and that is what comes recorded in the shift of the spectra. The photons themselves follow the general relativity geodesics. The expansion of the space they travel through is taken care in the geodesic.
The shift is the doppler shift:
The Doppler effect (or the Doppler shift) is the change in frequency or wavelength of a wave in relation to observer who is moving relative to the wave source
It is an effect of coordinate transformations needed between observer and source.