Holmes very definitely killed nowhere near as many people as recent writers, led by Herbert Asbury and Erik Larson, have suggested. Asbury, writing in 1940, was the first to suggest that Holmes's victims might have numbered "several hundred," the figure commonly encountered online today. Larson dismissed speculation that the number of victims might have reached 200, but his book incorporates a vast array of errors that were not properly checked when lifted from earlier authors. Adam Selzer is pretty damning about the methodology that Larson used in his bestselling The Devil in the White City

The vast majority of these supposed murders are supposed to have taken place in the infamous "castle" – actually a lodging house – that Holmes constructed in Chicago in time for the 1893 World's Fair, which sensationalist account suggest was purpose-equipped with torture equipment, suffocation chambers, dissection tables, vats of acid, and lime pits for the disposal of bodies, but these cases were for the most part barely investigated at the time they are said to have occurred, and became attached to Holmes's legend only after his arrest and death.

Most recently, meticulous primary research by Selzer has shown that a significant number of his alleged victims were definitely alive after the date of their claimed deaths and that it's impossible to prove that anyone actually died in the "murder castle". The murders that Holmes was actually hanged for – those of three children named Pietzel and their father, the latter being a Holmes associate caught up in an insurance fraud – took place in Toronto in 1894.

Selzer concludes that

Holmes was proven to have murdered only one person – and even then, the evidence was mostly circumstantial. A lack of data makes most of the other suspected murders difficult to truly confirm. There are four people whom we can be quite confident he killed personally, then five more whom we have no reason to doubt, though the evidence isn't strong enough that he could have been convicted.

Beyond that, there are any number of victims suggested by newspapers or by Holmes himself. Most of these stories were never seriously investigated by the authorities, and there's usually not enough information left to research them in depth.

The five presumed murders mentioned by Selzer were those of women with whom Holmes had relationships, and they are also assumed to have been killed for insurance. They were Julia and Pearl Connor (1891), Emeline Cigrand (1892) and Minnie and Nannie Williams (1893).

Source

Adam Selzer, HH Holmes: The True History of the White City Devil (2017)