The h-index is often used to measure a 'quality' of a scholar, and it is also often criticized as a lousy measure, since there is more into quality than just the number of papers and citations.
What are some examples of arguably great and famous scientists with low h-index?
You can find a lot of historical examples, from people whose careers predated the publish-or-perish culture. A striking more recent example is Peter Higgs, who was awarded (among other honors) the 2013 Nobel prize in physics. Whether that makes him a "great" physicist is of course arguable, but he clearly did important work. However,
Peter Higgs, the British physicist who gave his name to the Higgs boson, believes no university would employ him in today's academic system because he would not be considered "productive" enough.
The emeritus professor at Edinburgh University, who says he has never sent an email, browsed the internet or even made a mobile phone call, published fewer than 10 papers after his groundbreaking work, which identified the mechanism by which subatomic material acquires mass, was published in 1964.
This article estimated his h-index to be about 9, but I've seen estimates of around 11 too. Either way, it's a very low number for the field by today's standards, for an established professor. To wit,
Speaking to the Guardian en route to Stockholm to receive the 2013 Nobel prize for science, Higgs, 84, said he would almost certainly have been sacked had he not been nominated for the Nobel in 1980.
Edinburgh University's authorities then took the view, he later learned, that he "might get a Nobel prize – and if he doesn't we can always get rid of him".
Here are a few contemporary mathematicians who solved major open problems and have relatively low h-index, computed using citation data MathSciNet, for their stature in the mathematical community:
Yitang Zhang (proved boundedness of gaps in primes): h-index 2
Grigori Perelman (solved the Poincaré conjecture): h-index 10
Andrew Wiles (proved Fermat's Last Theorem): h-index 15
All of these mathematicians made quite the splash, and are worth reading about, and have the feature that they wrote relatively few papers but worked on very deep, hard problems.
Ernst Ising probably counts. He did his PhD thesis on the (now well-known) model that bears his name, but didn't work in physics for decades afterwards. Though he eventually became a physics professor, he didn't publish again either. I couldn't find anything about his h-index, but it can't be too high since there aren't many works written by him.
After earning his doctorate, Ernst Ising worked for a short time in business before becoming a teacher, in Salem, Strausberg and Crossen, among other places. In 1930, he married the economist Dr. Johanna Ehmer. As a young German–Jewish scientist, Ising was barred from teaching and researching when Hitler came to power in 1933. In 1934, he found a position, first as a teacher and then as headmaster, at a Jewish school in Caputh near Potsdam for Jewish students who had been thrown out of public schools. Ernst and his wife Dr. Johanna Ising, née Ehmer, lived in Caputh near the famous summer residence of the Einstein family. In 1938, the school in Caputh was destroyed by the Nazis, and in 1939 the Isings fled to Luxembourg, where Ising earned money as a shepherd and railroad worker. After the German Wehrmacht occupied Luxembourg, Ernst Ising was forced to work for the army. In 1947, the Ising family emigrated to the United States. Though he became Professor of Physics at Bradley University in Peoria, Illinois, he never published again. Ising died at his home in Peoria in 1998, just one day after his 98th birthday.
How about a physicist, Erich Hückel, who created Huckel theory and one of the founding fathers of Molecular-Orbital theory / quantum chemistry.
He was definitely someone who struggled in academia even before the publish-or-perish era, hardly able to get a professorship. I couldn't find his official publication list, but this encyclopedia article lists 11 works for all his life: https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/huckel-erich-armand-arthur
Just yesterday this article was published with the title "Albert Einstein the mediocre: Why the h-index is a bogus measure of academic impact." Check this out:
"let's examine the case of Einstein, who has 147 articles listed in the Web of Science database between 1901 and 1955, the year of his death. For his 147 articles, Einstein has received 1,564 citations during his lifetime. Now, if we add the citations made to his articles after his death, Einstein has received a total of 28,404 citations between 1901 and 2019, which earns him an h-index of 56."
Only 1564 citations over 147 articles, at the time of his death!
The h-index of 56 might seem large, but there's been about 70 years of citations (23,000 of them) after his death, so even when he was 76 years old he would have had an h-index that might be considered mediocre for someone at that age, and someone considered to be one of the most prolific academics of all time.
Incidentally, to answer the question in the title, "scholarship" and "peer-reviewed publication" are substantially different things, somewhat like "understanding" and "novelty" are not at all the same, though loosely connected.
In mathematics, in the U.S., for example, "scholarship" is not much rewarded by "the system", if only because it's hard to quantify, and the contemporary style of quantification of is much beloved by administrators at all levels, and papercount, etc., are numbers.
And, then, again, "citation count" is a very skewed metric, for many reasons.
