As the Arab Spring spread to Libya, the United States and its European allies took advantage of Gaddafi’s weakness and organised his overthrow to kill him.
After the defeat of ISIS, the Americans changed their tactics in order to use this terrorist group for guerrilla/subversive activities.
There is no evidence that the US has supported radical Islamist terrorist groups in Syria. The US-led military campaign in Syria has been fighting ISIS and Islamic terrorists along with the Global Coalition Against Daesh. Background and a similar case can be seen here and here.