Somehow it was Trump who brought up Ted Cruz's place of birth. And his father was also a Cuban. It was his mother who was American. 

The Democrats never brought up McCain's place of birth. But in the 2000 primaries, GW Bush's team passed out a rumour that McCain's adopted Bangladeshi child was his love child with a black woman. That caused him to lose the South Carolina primary, and other primaries. 

https://www.vanityfair.com/news/2004/11/mccain200411

McCain's daughter stated in an interview that her family refused to vote for GW Bush in 2000 and 2004, due to this underhanded tactic.