[steven]

OK, I apologize. I misinterpreted what you said. In that case, it would fall under "hiragana". In the case of hiragana, though, you only see certain "small" kana.

As far as I know, you only see っ (small tsu), ゃ, ゅ, and ょ. Sometimes you'll see things like ぁ, but that would be for things like わぁ～, which isn't exactly a word, persay.

"じぉうし", as far as I know, should probably be written as "じょうし”.

This is an area where hiragana and katakana differ. With katakana, you'll often see a lot of "small" kana that you'd normally not see in hiragana. (Sometimes you'll see "katakana words" written in hiragana. In fact, old video games do this a lot.

Here are some examples of using small katakana in situations where you wouldn't usually do it with hiragana.

ジェット
ジェスチャー
チェキ
パーティー
スティーブン/スティーヴン (notice the "ten ten" on the ウ, which would be unusual for hiragana)
トゥーズデー　(as opposed to チューズデー)

Incidentally, although it may be different from what is "normal" you sometimes see English words "transcribed" into katakana with the use of "small" kana.

フレンド This would indicate to the reader that you shouldn't pronounce the vowel end of the ド. I imagine that most people aren't famliar with that though. I've also seen it done with a small ッ written at the end of the kana (this might actually be less uncommon).