I don't know how to pick the point directly, but if faced with the same problem, I would create section curves based on a plane that runs through the axis of the cone then pick the end of the curves. See attached.
Not sure what operation that you're performing but lets say it's something like wanting position the center of a Sphere feature at the apex of the cone. So when the Sphere dialog opens and you're in the 'Center Point and Diameter' Type, instead of just trying to use either the 'Inferred' point method or by setting any of the 'Snap Points' from the Selection Bar, simply select 'Point Dialog' icon in the the 'Center Point' section of the dialog and when the 'Point' dialog comes up, from the Type list, select the 'Point on Face' option. Now select a point anywhere on the conical face and then in the section of the dialog titled 'Location on Face', enter the value of '0.00' for both the 'U Parameter' and the 'V Paramter' and hit OK. You should have a point 'handle' displayed at the apex of the cone and you can now complete your creation, whatever that might have been.
John R. Baker, P.E.
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