step on, tread on, search for
跴 centers on the action of stepping or treading on something, with a secondary sense of searching that likely extends from the idea of treading over ground while looking.
跴 combines 足 (foot) with 西, which likely contributes the sound. The exact historical development is uncertain, but the structure suggests a phono-semantic compound related to foot action.
The left side is a foot 足, and the right side looks like a western 西 boot. Picture a heavy western boot stepping down and treading over the ground as you search for something.
For サイ, imagine a sigh of frustration as you step on something unpleasant: sigh -> サイ, and your foot treads right into it.