Scott

Wilkinson

In a word, no.

In 1791, there were eight or more sites were under consideration to become the capital of the new state of Kentucky.  Only four of these were seriously considered, and one of the four was Petersburg.  However, the Petersburg that was under consideration was not in Boone County, but in Woodford County.

The Woodford County town was laid out by General Charles Scott(Wikipedia), with anticipation of it becoming the capital.

The legislature at the time opted to make the capital whichever town anted-up the most, and Frankfort, under the leadership of the infamous General James Wilkinson (Wikipedia), came up with land, rent from a tobacco warehouse for 7 years, building supplies, and $3,000 in gold.  No place else was even close.

General Scott went back to fighting Indians, and today, you'll look hard to find Petersburg on a current Woodford County map.

The Petersburg in Boone County was never a candidate.  Sorry.