The Ohio River is a ranking boundary, not a line on your service map
A searcher in New Albany gets New Albany results, and no amount of content moves your Kentucky pin across the bridge.
Local search leans hard on where the person is standing. Someone typing from Jeffersonville sees businesses near Jeffersonville. Your Jefferson County address does not travel, and page quality will not overcome the distance in the pack.
If you hold licensing on both sides, the Indiana work needs its own pages. Jeffersonville, New Albany and Clarksville each deserve real content: jobs you have done there, the neighborhoods you cover, the way you handle a Clark County or Floyd County call. Generic Kentuckiana copy ranks for nobody and reassures nobody.
If you only work Kentucky, say it plainly on the site and stop spending effort on Indiana terms. Licensing, tax and registration requirements differ by state and are worth confirming with the state boards or your own counsel. Advertising into work you cannot legally take is expensive in a way no report shows.
There is a middle case. Some shops take planned Indiana work but not emergencies, because the bridge crossing kills the response window. Write that down on the page. Buyers respect a limit more than they respect a vague promise.