In Air Force One a fighter jet maneuvers between a missile and the president's plane, as shown in this clip.
Is such a maneuver possible?
If not, what could be done in that situation?
Possible and Plausible are two different things.
Is it possible to fly a fighter jet between a missile and another aircraft, and either (a) confuse that missile so it follows the fighter instead) or (b) have the fighter be hit by the missile instead of the original target aircraft? Yes.
Modern fighters are capable of maneuvering in the manner shown: they can even sustain knife-edge flight or vertical climb for a while. It's even possible that in a moment of desperation a pilot would attempt such a maneuver, sacrificing themselves and their aircraft to save their commander-in-chief.
(The G-forces involved in these maneuvers may be unpleasant or even unbearable for the pilot, but if you're committing yourself to a course of action that ends with your plane blowing up to save another plane the G-forces are probably the least of your concerns.)
It isn't plausible that such a maneuver would work - at least not as depicted in the movie.
Missiles are REALLY FAST - this footage includes several slow motion shots of an air-to-air missile as it's fired (at it's slowest relative velocity), and it's still pretty darn quick: It's gone in a few frames of high-speed footage.
For this maneuver to work the intercepting pilot would need to be in exactly the right position and exactly the right time, and perform the maneuver perfectly in order to intercept the missile: A little error in any direction - too fast, too slow, too far left, or too far right - and the missile would fly right past them and continue on toward its target.
The intercept is further complicated by the fact that, assuming the missile is guided, both the missile and the target are maneuvering as well.
(If it's a non-guided "dumb" missile all the target aircraft needs to do is change course to avoid being hit - a maneuver that might stress the airframe a bit, but certainly less than being hit by a missile would.)
To give a little more context, the "anti-missile missile" programs have often been described as having your friend throw a baseball over the roof of your house while you stand on the other side and try to hit it with a golfball as it comes over the top.
This intercept is of similar difficulty, except the balls involved are all steering themselves toward different objectives.