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I read this expression in Sherlock Holmes: A Study in Scarlet. The chapter is about a man and his adopted daughter both are living amongst Mormons.

“It was a warm June morning, and…[d]own the dusty highroads defiled
long streams of heavily laden mules, all heading for the west, for the
gold fever had broken out in California, and the overland route lay
through the city of the Elect.”

In the link below the author discusses the historical accuracy of the novel and again mentions about the same city (Beginning from the last line of page #31).

http://www.bakerstreetjournal.com/images/2000%20American%20Chapters%20-%20Vizoskie.pdf

There were westward travelers through the City of the Elect, but
they were silver miners headed for Nevada—the Comstock Lode had been
discovered in February, 1859.

It seems the author knows this city too but my Google search haven't furnished me with a good answer to my question. Is it the real name of a city? If not what does this refer to?

As a side question how should I interpret the sentence I quoted from the book?

Option 1: ... all heading for the west for the gold fever had broken out in California and they will firstly reach the overland route lay through the city of the Elect and will travel to California via this route

Option 2: ... all heading for the west for the gold fever had broken in California and the gold fever had broken in the overland route lay through the city of the Elect

I would presume, since you mention Mormons, that the "City of the Elect" refers to either Salt Lake City, or possibly an earlier home of the LDS, such as Nauvoo.

I cannot make sense of either of your paraphrases. I think you must be misunderstanding either certain words or certain constructions, but I can't make out what.

Try this:

all heading for the West,

[parenthetical clause:] for the gold fever had broken out [emerged, become an epidemic] in California,

and the overland route [from where they started, leading to the West] lay through the C of the E.