Shortest distance between a coordinate and a walking path in osm

Is there an online API to calculate shortest distance between a coordinate and 1 (or more) walking paths in osm? I am especially interested in even the smallest paths that are visible on osm

I don’t really understand your question.

Routes are found between coordinates, not paths. It might use a path if it’s on the shortest path. But there’s no way of deterministically making sure it uses a specific path, that would defy the implications of ‘shortest’.

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