While Turkey has certainly leveled elaborate allegations against Gulen and the US government, these theories have never included much evidence. Gulen was a controversial figure whose history includes both positive and negative relations with Pres. Erdogan. Given that Gulen and Erdogan were both secularists, their differences were likely connected to the corruption charges laid against the president rather than religious beliefs.
Gulen’s long-standing ties to US interests, including alleged links to American intelligence agencies, make it completely reasonable to question whether he and Western intelligence agencies orchestratd a coup together. Besides his residence in Pennsylvania and Washington's refusal to extradite him, testimonies in Turkey confirm his followers were working to destabilize the Turkish government.