There are those who say that apostrophes are for contractions, possessives, and even plurals. That's not quite right. The apostrophe, from the Greek turn away, refers to something removed.
In the 16th century, English adopted the apostrophe from the French, using it to represent letters that had been omitted. When people started saying I'm instead of I am and shan't instead of shall not, the apostrophe stood in for the letters that had been taken out. Often, this had to do with the way the word was pronounced, leading to spellings like walk'd for walked, or more extreme contractions such as fo'c'sle for forecastle (which is part of a ship).
In modern English possessives, where we use the good old apostrophe-s, the apostrophe still stands for something taken away.
As early as the late 1200s, one way of expressing possession was the word his, something like *the king his son (the king's son). A competing form (and competing theory)1 relies on a genitive case2 formed in Anglo-Saxon by adding -es or -ys, and pronounced just like the word his was at the time: the kyngges sone. Toward the end of the 1500s, the his genitive reappeared as a hypercorrection, disappearing again by around 1700 as the apostrophe began to take hold. The study of these possessive forms has been hampered by the scarcity of definitive data, and the relationship between the two is a bit unclear.3
In any case,4 the apostrophe nearly always stands for something that has been taken away. That's why there's no apostrophe in the possessive its. Like the other possessive pronouns her, hers, his, my, mine, our, ours, their, theirs, your, and yours, no letters need to be removed. These pronouns, the last holdouts of the English genitive case, already indicate possessive through their form. When you say Ralph's book, you are using a contraction for a form such as *Ralphes book or *Ralph his book.5 When you say his book or its pages, you are not forming a contraction at all.
The exception proves the rule. There is one time when an apostrophe marks space to reduce confusion, but doesn't stand for anything taken out: the plural of a single letter. Whether you're minding your p's and q's6 or going to an A's7 game, it's proper to use an apostrophe.
See What's a Case?
Shinkawa, Seiji. “His-Genitive as a Morphological Variant of S-Genitive: An Analysis of Early Examples in the Otho Manuscript of Laȝamon's ‘Brut.’” Neuphilologische Mitteilungen, vol. 114, no. 4, 2013, pp. 473–480. JSTOR, www.jstor.org/stable/43346346. Accessed 28 Apr. 2021
But we’re talking about the genitive case.
There were also less common forms that included ender agreement: *the queen her throne, and that sort of thing.
The Google developer documentation style guide recommends capitalizing single letters referred to in this way. However, p's and q's only need minding when they're lowercase.
Image: a tiny quarter inch GREEN ROSETTA at the summit of a dense but radiant muffin of my own design.
One could argue that the apostrophe stands for “thletics.”
"The crux of the biscuit"?
Peter, in the second paragraph I think you mean "pronounced" but autocorrect gave you "produced"? Am I right?