Sorry, you’ve lost me here? Climb vertically? Pretty much any fighter aircraft can do that.
If you mean “accelerate” in the vertical, then yes, the F-15C can do this, but only at light fuel loads and with no stores fitted ( no external tanks, no weapons ). As long as the all up weight is less than the combined thrust from the two engines, then the F-15C will accelerate even in a vertical climb. The F-15E is too heavy to accelerate in the vertical.
However, you cannot rely on the indicated airspeed for this, as IAS reduces with altitude, so it may look as though you’re slowing down, but you’re not - the air is just getting thinner as you climb. Mach number is all that matters.