ALBANY — Aides to New York’s first African-American governor wanted a police entourage that looked more like their boss, so they made an unusual request to the State Police: Replace at least 10 white troopers assigned to protect Gov. David A. Paterson with black or Latino officers. The request prompted an extraordinary battle between the Paterson administration and leaders of the State Police shortly after Mr. Paterson, a Democrat, took office in 2008, according to court testimony, e-mails and interviews. Preston L. Felton, at the time the acting superintendent of the State Police and the first African-American to lead the...