子 Zǐ is an old word for child:
Nowadays one sees it more as a suffix; it loses its tone: zi, e.g. 句子 jùzi 'sentence'
仔 Zǐ is 'young (of animals)' or 'meticulous':
Common word: 仔细 zǐxì 'careful'
字 Zì is 'character, letter'
Think of a child under a roof learning characters.
Common word: 汉字 Hànzì 'Chinese character'