How to extrude a sketch which is projected on to a surface

If the curve is not in a plane then it cannot be projected to create a surface.

However, you can create a surface using the curve as a trajectory, setting the orientation direction, and using a sketched line to represent the projection.

(edit to clarify surface creation.)

Please provide an illustration of what you are trying to accomplish.  It is very likely that there is a way to do it.

Creo Parametric can only extrude planar curves that are sketch features directly. It uses the sketched curve for the extruded geometry and the plane it's sketched on for direction.

If you've made a sketch, projected it onto a curved surface, that new shape can be extruded but you'll need to create a new sketch from those curves on a plane that represents the new extrude direction. So, create a new sketch on a plane representing the direction you want to extrude and use the "project" tool in sketcher to convert those 3D curve entities to 2D projections on the new plane.  This sketch can then be extruded.

Essentially, you need to project what you projected onto a new plane in order to extrude it.