Are assistant professors or adjunct faculty eligible to apply for the American Postdoctoral Research Leave Fellowship??

Yes, provided they meet all fellowship eligibility requirements. Appointment titles vary by institution and discipline and do not, by themselves, determine eligibility.

For this fellowship, a "postdoctoral appointment" is an eligible academic or research appointment that provides an appropriate environment to conduct postdoctoral research. Eligible appointments may include Assistant Professor, Adjunct Faculty, Visiting Assistant Professor, Research Associate, Research Fellow, Postdoctoral Fellow, Lecturer, and similar academic or research positions.