It looks like a lot of people are convinced of quantized redshifts. This is part of an article I wrote for wikipedia:
Quantization of redshifts
Many in the fringe and completely outside of the scientific mainstream have made noise surrounding the idea that observed redshifts are quantized. A large percentage of these people explicitly reject the Big Bang model of the universe and try to explain the Hubble Law Expansion observed relationship that connects redshifts with distance as being due to alternative effects. Modern geocentricists have also joined in, hoping to use the quantization of redshifts as proof, not of an incorrect redshift-distance relation, but rather as an indication that our observing point is the center of the universe. As it stands now, there is no evidence for redshift quantization, so the enterprising geocentrist must look elsewhere for evidence that we are at the center of the universe.
The first claimed observations of quasar redshift quantization came in 1976 by astrophysicist Y.P. Varshni. He presented his data with three possible interpretations, one of which is that Earth was in the center of the universe. Varshni wrote (in Astrophysics and Space Science, 1976, 43:3)
... the quasars in the 57 groups ... are arranged on 57 spherical shells with the Earth as the center ... The cosmological interpretation of the red shift in the spectra of quasars leads to yet another paradoxical result: namely, that the Earth is the center of the universe. The arrangement of quasars on certain spherical shells is only with respect to the Earth. These shells would disappear if viewed from another galaxy or quasar
Varshni calculated the odds against a chance arrangement of 57 concentric spheres of quasars around the earth to be 3 x 1086 to 1. This, unfortunately, is an example of an eggregiously misleading miscalculation based on faulty Bayesian priors. Varshni ultimately attributed his results to an intragalactic (that is, non-cosmological) location of the quasars and a redshift resulting from a laser phenomenon rather than cosmological expansion.
In 1970, William G. Tifft, astronomer at Steward Observatory at the University of Arizona showed that a few dozen galaxies were situated from Earth at specific redshifts, namely, in multiples of 72 km/sec in redshift values, as recorded in "Global Redshift Periodicities: Association with the Cosmic Background Radiation" Astrophysics and Space Science, 239, 35 (1996), and "Evidence for Quantized and Variable Redshifts in the CBR Rest Frame," Astrophysics and Space Science, 1997. Even today, Tift continues to insist on a quantization of local galaxies' redshifts. In 1992, Sky and Telescope magazine gave coverage to Tifft's ideas and extrapolated a possible geocentric interpretation to his fitted data ("Quantized Redshifts: What's Going on Here?" 84:128, 1992). At that time there was considerable controversy surrounding seeming contradictions that had arose in the Big Bang model which have since been resolved by the observational concordance of the Lambda-CDM model. Tift's work has subsequently been shown lacking in scope and in believability by the vast amounts of new data from galaxy surveys which show no statistical evidence for redshift periodicity of galaxies.
Other references to the same type of work on quantized quasar and galactic redshifts, are Tifft and Cocke writing of this phenomenon in Sky and Telescope, 73:19, in 1987 in the article "Quantized Galaxy Redshifts," as well as in New Scientist of June 22, 1985, in the article "Galaxy Redshifts Come in Clumps." Burbidge wrote about the same phenomenon in Mercury in the article "Quasars in the Balance," 17:136 in 1988. Halton Arp has provided the most information in his book "Quasars, Redshifts and Controversies." He and Burbidge wrote of their work in Physics Today, 37:17 (1984) in the article "Companion Galaxies Match Quasar Redshifts: The Debate Goes On." In 1991, astronomers Bruce N. G. Guthrie and William M. Napier of the Royal University at Edinburgh compared the redshifts from 89 single spiral galaxies and found a periodicity that was very close to Tifft's quantum multiple for this class of galaxies. At the time, 89 galaxies seemed like quite a lot, but it pales in comparison to the hundreds of thousands of galaxy redshifts measured as of today.
It happens that all of these analyses suffer from either poor data-fitting models or bad statistics. Currently, with today's collections of galaxy and quasar redshifts from galaxy surveys, there is absolutely no statistically detectable evidence found for quantization of redshifts. Sky and Telescope reported this finding conclusively in its 2002 issue ("No Quantized Redshifts" 104:28, 2002). The "controversy" has been laid to rest, and only a few hangers-on such as Halton Arp and William Tift continue to ignore the vast preponderance of the evidence from modern sky surveys. The most recent, most complete, and most accurate measurements of quasar redshifts do not support a distribution of galaxy and quasar "celestial spheres" centered on our location. Indeed, as galaxy surveys have been collecting more and more quasar counts, the quantization coincidences are not seen as model phenomena.