what controversy did he have during his career?
It was a dispute with Sony Music who tried to release an album with some of his unreleased songs after his contract with the label had ended.
Alejandro Fernández
The international record label Sony Music was sued by Alejandro Fernández after they tried to release an album with some of his unreleased songs after his contract with the label had ended. 
what is  me estoy enamorando (album)? It is the sixth studio album by Alejandro Fernández. where is this musician from? Guadalajara, Jalisco , Mexico. what are some music he was famous for? Some of his famous albums were "Alejandro Fernandez", "Piel de Niña" ,"Grandes Éxitos a la Manera de Alejandro Fernández", etc.
wiki:20183362
Alejandro Fernández [SEP] "Sony Music" controversy
The international record label Sony Music was sued by Alejandro Fernández after they tried to release an album with some of his unreleased songs after his contract with the label had ended. Federal Police arrived at the Sony headquarters in Mexico City and seized about 6,000 copies of the album. The song "Diferente", was released on the internet as the first single of the album.