じ and ず are used basically. ぢ and づ are used in the next case. 1. 同音<どうおん>の連呼<れんこ>によって生じた「ぢ」「づ」 ぢand づ caused by calling repeatedly homophony Examples ちぢに<千々に> in pieces / variously ちぢこまる<縮こまる> to cower ちぢまる<縮まる> to shorten　※intransitive verb ちぢむ<縮む> to shrink　※intransitive verb ちぢめる<縮める> to shorten / to shrink　※transitive verb ちぢれる<縮れる> to be wavy / to be curled つづく<続く> to continue　※intransitive verb つづける<続ける> to continue ※transitive verb つづみ<鼓> hand drum つづら<葛籠> wicker つづる<綴る> to spell 2. 二語の連合によって生じた「ぢ」「づ」 ぢand づ caused by the coalition of two words ※The latter word still retains the meaning. Examples みぢかな<身近な> familiar ← み＋ちか＋な ちかぢか<近々> soon ← ちか＋ちか きづく<気付く> to notice ← き＋つく はなぢ<鼻血> nosebleed ← はな＋ち いえづくり<家作り> house making ← いえ＋つくり たんちょうづる<丹頂鶴> sacred crane / Japanese crane ← たんちょう＋つる ※for your information http://www.mext.go.jp/b_menu/hakusho/nc/k19860701001/k19860701001.html

I think you are talking about じ and ぢ、ず and づ. They are a part of one word so you have to memorize them. Ex.) じかん(時間)、かんじ(漢字)、みぢかな(身近な)、ちかぢか(近々)、ちず(地図)、すこしずつ(少しずつ)、つづく(続く)、きづく(気づく) etc I hope this was helpful. Good luck!