Sharing some thoughts.
Although very long range AAM's like the Russian Novator KS-172 have been developed and can theoretically target high value assets like the AWACS aircraft, they are of little use in bringing down modern fighter aircraft. Since the AAM's are relatively big in size and need to carry enough fuel for achieving the extra range. They hence become less maneuverable and incapable of very high G turns. Modern fighter aircraft can probably out maneuver them.
Now to overcome this limitation.
Probably an air to air missile can be made which will actually consist of two missiles. Just like how our space launch vehicles like the PSLV and GSLV carry booster engines which are jettisoned in flight, an booster like mother missile can carry an smaller child missile which will have all of the sensors and propulsion systems like any normal AAM. The mother missile will be used to get close to the fighter size target, maybe at ranges < 100 km using its own guidance systems and mid course guidance updates by the launching aircrafts radar.
At an stipulated distance from the target fighter the smaller air to air missile probably carried in the belly of the mother missile will activate its sensors and get a lock on to the enemy fighter. Once the lock on is achieved, the mother missile will eject the child missile which will then proceed to the target under its own power. It should have sufficient fuel and good sensors to be able to chase the enemy fighter and bring it down.
The technical challenges are many and whether something like this is feasible remains to be seen.