While
中（ちゅう）に highlights that something is in the process of happening (when used in relation to events/actions),
最中（さいちゅう）に strengthens that meaning further, to show that something is ‘right in the middle of happening’. As the kanji 最（さい） means ‘utmost’, we can see that the literal meaning is ‘utmost middle’. This can be translated in a similar way to phrases like ‘at the height of (A)’, or ‘in the midst of (A)’, in English.
When using
最中（さいちゅう）に, a (B) part of the sentence will usually highlight something else that happened during (A), somehow interrupting or disturbing it.
To use
最中（さいちゅう）に, attach it to the end of the ている form of a verb, or a noun followed by の.
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お祖母（ばあ）ちゃんの歯（は）がお餅（もち）を食（た）べている最中（さいちゅう）にポロっと取（と）れた。
Grandma’s tooth fell out right in the middle of eating mochi.
仕事（しごと）の最中（さいちゅう）に怪我（けが）をしたら、黙（だま）っていないですぐに責任者（せきにんしゃ）に電話（でんわ）をしてください。
If you get hurt in the middle of work, please don’t keep it to yourself and notify your supervisor.
今（いま）、犯人（はんにん）を追（お）いかけている最中（さいちゅう）だ。
Right now, I'm in the midst of chasing a criminal.
最中（さいちゅう） may also occasionally be used with adjectives, but this is uncommon. In these cases, the meaning is to be at the ‘pinnacle’ of whatever the adjective is describing (usually a feeling/emotion).
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冗談（じょうだん）でも悲（かな）しい最中（さいちゅう）に悪口（わるぐち）を言（い）われると、もっと悲（かな）しくなる。
Even if it is a joke, when someone says something mean when I am really sad, I get even more sad.
一生懸命（いっしょうけんめい）な最中（さいちゅう）に話（はな）し掛（か）けられると、一気（いっき）に集中力（しゅうちゅうりょく）がなくなる。
When someone talks to me when I am highly concentrated, I suddenly lose my concentration.