I'm looking for a synthesizer to play some music which includes quarter tones, like Arabic music.
Does anyone know what synthesizers have this option, please ?
I found a list here but I don't know if quarter tones are available on them.
See my answer at the link below, where I give a list of keyboards that meet your criterion, from Casio, Roland, Korg, Yamaha, and Generalmusic.
All of these keyboard instruments have the word "Oriental" or "Middle-Eastern" in the name of the product.
Most synthesizers have a pitch bend wheel that will allow you bend the pitch up or down by a number of microtonal increments. The trick is to train your ear and your hand to coordinate the proper microtonal adjustment on the fly as in the way a violinist develops intonation.
A more expensive synthesizer may allow you to set the keyboard to a particular tuning system that might be a better fit for the scales you are trying to play.
I highly recommend that you first learn to sing the notes correctly before embarking in using a pitch bending wheel as this will improve your musicianship instead of relying solely on the technology.
Consider too, how guitarists are able to create micro tonal pitches by bending the string at the nearest scale degree to play alternate scales.