I noticed this coincidence and I couldn't help wondering since other parts are based off of Chinese(kanji)
No, it's a coincidence. ゆ is over a thousand years old and is thought to be derived from 由. You can find a chart of the kanji that hiragana developed from on Wikipedia.
Mandarin yú is more recent and corresponds to Japanese 魚 gyo, both of which developed from Middle Chinese ngyo (where the digraph ‹ng› represents the nasal velar sound [ŋ], as in English ring). At the time ゆ developed, the sound was too different from yu to make this kind of connection.
Hiragana ゆ developed from the kanji character 由 (see for example this).
Japanese on-yomi reading of kanji 魚 is ぎょ and there is no relation to the Chinese yu.