Two Yuds in a row designate the name of God Adonai and in pointed texts are written with the vowels of Adonai; this is done as well with the Tetragrammaton.
As Yud is the smallest letter, much kabbalistic and mystical significance is attached to it. According to the Gospel of MatthewJesus mentioned it during the Antithesis of the Law when he says: "One jot or one tittle shall in no wise pass from the law, till all be fulfilled." Jot, or iota, refers to the letter Yud; it was often overlooked by scribes because of its size and position as a mater lectionis. In modern Hebrew, the phrase "tip of the Yud" refers to a small and insignificant thing, and someone who "worries about the tip of a Yud" is someone who is picky and meticulous about small details.
Much kabbalistic and mystical significance is also attached to it because of its gematria value as ten, which is an important number in Judaism, and its place in the name of God. See The Mystical Significance of the Hebrew Letters - Yud.
In Modern Standard Arabic it is a part of a diphthong, /aj/. In this case it has no diacritic, but could be marked with a sukun in some traditions. The preceding consonant could either have no diacritic or have fatḥa sign, hinting to the first vowel in the diphthong, i.e. /a/.
As a vowel, yāʾ can serve as the "seat" of the hamza: ئ
Yāʾ serves several functions in the Arabic language. Yāʾ as a prefix is the marker for a singular imperfective verb, as in يَكْتُبyaktub "he writes" from the root ك-ت-ب K-T-B ("write, writing"). Yāʾ with a shadda is particularly used to turn a noun into an adjective, called a nisbah (نِسْبَة). For instance مِصْرMiṣr (Egypt) → مِصْرِيّMiṣriyy (Egyptian). The transformation can be more abstract; for instance, مَوْضَوعmawḍū` (matter, object) → مَوْضُوعِيّmawḍū`iyy (objective). Still other uses of this function can be a bit further from the root: إِشْتِرَاكishtirāk (cooperation) → إِشْتِرَاكِيّishtirākiyy (socialist). The common pronunciation of the final /-ijj/ is most often pronounced as [i] or [iː].
A form similar to but distinguished from yāʾ is the ʾalif maqṣūrah (أَلِف مَقْصُورَة) (broken alif), with the form ى. It indicates a final long /aː/.
In Egypt, Sudan and sometimes Maghreb, the final form is always ى (without dots), both in handwriting and in print, representing both final /-iː/ and /-aː/. ى representing final /-aː/ (DIN 31635 transliteration: ā) is less likely to occur in Modern Standard Arabic. In this case, it is commonly known as, especially in Egypt, أَلِف لَيِّنَةʾalif layyinah[ˈʔælef læjˈjenæ]. In Egypt, it is always short [-æ, -ɑ] if used in Egyptian Arabic and most commonly short in Modern Standard Arabic, as well.
In Perso-Arabic the letter is generally called ye, following Persian-language custom. In its final form, the letter does not have dots (ی), much like the Arabic ʾalif maqṣūrah or, more to the point, much like the custom in Egypt, Sudan and sometimes Maghreb. On account of this difference, Perso-Arabic ye is located at a different Unicodecode point than both of the standard Arabic letters.
Position in word:
In computers, the Persian version of the letter automatically appears with two dots initially and medially: (یـ ـیـ ـی). The Arabic version without dots ى isn't used initially or medially and it isn't joinable initially or medially in all fonts. However, it is used in the Uyghur Arabic alphabet and the Arabic-based Kyrgyz alphabet: (ىـ ـىـ).
Position in word:
In Kashmiri, it use a ring instead from ي of a dots below (ؠ ؠـ ـؠـ ـؠ).
In Nastaʿlīq calligraphic style a final yāʾ might have a particular shape (ـے), either with two dots or without them.
In Urdu this is called baṛī ye ("big ye"), but it's an independent letter used for /ɛː, eː/ and differs from the basic ye (chhoṭī ye, "little ye"). For this reason the letter has its own code point in Unicode. Nevertheless, its initial and medial forms are not different from the other ye (practically baṛī ye is not used in these positions).