The Adam’s apple (also known as the “laryngeal prominence”) is an important gender sign. Despite what many people believe, it is sometimes visible in females but in males it can be very prominent.
The Adam’s apple can be reduced with a procedure often referred to as a “tracheal shave” or “trach shave”. The technical name for this procedure is “chondrolaryngoplasty” but you may also hear of it referred to as “thyroid cartilage reduction” or “TCR” for short.
The incision is sometimes made in the neck directly over the adam's apple. As with all surgical incisions, this will leave a scar but the surgeon usually makes the cut run along one of the natural creases in the skin and that helps minimise the appearance of the scar. Do bear in mind that the surgeon does not have complete control over the scar - some people scar more than others and some people might scar badly on one occasion and only slightly on another. The alternative is to make the incision under the chin - the surgeon then tunnels down to the Adam's apple under the skin. The advantage of this is that the scar is much less visible as it's hidden under the chin. Normally, a tracheal shave will not raise the pitch of the voice.
The cartilage that forms the Adam’s apple tends to harden with age and that may limit the amount that can be removed in an older patient. There is also a limit to how much can be removed without risking permanent damage to the voice. Basically, the Adam's apple is part of the front wall of the voice box and the vocal chords are attached to that wall - if the wall is thinned too much, it may no longer be strong enough to hold the vocal chords in full tension. This can leave the voice deeper and with a gravelly sound.
Tracheal shaves seem to carry a higher risk of complications than most other FFS procedures and should always be considered very carefully.
This is the Wikipedia article on the Adam's apple: