Summary: Let \(Y\subset \mathbb {P}^n\) be an integral curve contained in a surface \(S\). When is the osculating plane of \(Y\) at a general \(P\in Y\) equal to the tangent plane of \(S\) at \(P\)? In positive characteristic we find for each ruled surface \(S\) a curve \(Y\) as above and classify all such \(Y\) if \(S\) is either a smooth quadric or a cone.