Highest altitude fighter kill

On 13 September 1985, US Airforce Major Wilbert D Pearson took part in an experimental flight dubbed the ‘Celestial Eagle Flight'. He piloted his F-15 fighter jet nearly vertically to an altitude of 10,600 m (35,000 ft) and fired a 5.4 m long (18 ft) anti-satellite missile up into space. The test flight was a success; the missile successfully intercepted and destroyed a retired US communications satellite, which was in Earth orbit at an altitude of 555 km (345 miles). This is the first and only time a satellite has been destroyed by a pilot.

Although it is a satellite being shot down, the technical term for anything being shot down is a "kill"