The movement, which controls 163 schools across the country and teaches around 70,000 students, has been accused of avoiding taxes.
FETO, a designated terror group in Turkey, has established itself abroad through companies, foundations, media outlets and charter schools.
The leader of the network, Fethullah Gulen is accused by Turkey of being behind a bloody coup attempt which left 249 people dead and more than 2,000 injured in the country last July.
Gulen, currently living in self-imposed exile in Pennsylvania, has denied the charge and continues to fight against Ankara's extradition demands.
His movement controls 163 schools across the country, teaching around 70,000 students. Now some schools linked to his network have come under investigation in the US over allegations of financial misconduct.
"In the state of New Jersey alone, a chain of charter schools is linked to the Gulen Movement, also known as FETO. The organisation's attempt to launch a fifth school in this state was denied, after the board of education said it had used "forged and fraudulent" petitions to show community support for its initiative," Ersin Konkur, a former maths teacher in a Gulen-linked school, told TRT World.
TRT World's Ediz Tiyansan has more.