Unknown what happened to the GEMS American school, and the only US curriculum school in Ajman worth considering for a western American education is the Deans International School - renamed as the Omadaa International School. There are other schools which advertise themselves as offering a US curriculum but they are generally for Arab Muslim students wanting a combination of Islamic and US curriculums. Consider traveling a bit further to one of the US curriculum schools in Sharjah.
American Academy in Ajman - doesn't exist, might be a reference to the Ajman Academy but that's an IB school.
American International School of Ajman - doesn't exist, might be a reference to Omadaa School in Ajman, or Sharjah American International School, or AIS Dubai.
Sama American School Ajman - doesn't exist, probably a reference to the Sama American School in Sharjah (which is a UAE MOE curriculum school anyway).