According to Persian phonology, hamze (glottal stop) is a glottal plosive consonant. A glottal consonant is articulated at the glottis, which is the opening between the vocal folds. Hamze is produced when the vocal cords are pressed together to stop the flow of air and then released. For example, the break separating the syllables of the interjection uh-oh. The glottal stop is present in nearly all dialects of English as a variant of /t/ e.g. button. The consonant h is another glottal consonant. Its place of articulation is glottis and only differs with hamze in the manner of articulation (fricative vs. plosive). You can use h as a starting point to learn how to articulate hamze.

The glottal stop is found in many languages but there is no character for it in Latin alphabet because in most Indo-European languages, the glottal stop only occurs at the beginning of a syllable. However in Persian, hamze occurs anywhere in a word and is indicated in writing. Hamze is usually denoted with an apostrophe in educational books and with its IPA sign (ʔ) in academic books. However, the apostrophe is not a letter but a sign. Moreover, its standard function is to indicate contractions:

Language Examples
English she's (she + is)
can't (can + not)
I've (I have)
French l'arbre (le + arbre)
c'est (ce + est)
Italian l'ora (la + ora)
po' (poco)
German geht's (geht + es)

Hamze is a sound and just like the other Persian sounds, should be denoted with a letter. I propose the letter ø and use it in all my works. The apostrophe is used for contractions.

Persian Latin Contraction
ابری‌ست abri'st abri + ast
زین z'in ze + in

It is obvious that apostrophe can not be used both for marking a contraction and marking a sound. This gives another proof for that hamze should be denoted with a distinct letter.

The apostrophe can also be used, for educational purposes, to indicate that adjacent consonants are separate and do not form a digraph

Persian Latin
مذهب maz'hab
اسهال es'hâl
برگها barg'hâ