Reddit reviews Saxophone High Tones

Easy answer: practice overtone exercises such as the classic:
fingering low Bb and changing your throat position to play a Bb up an octave, and then F a 5th above that, and Bb a 4th above that, etc.

Personal experience: what I found while developing my control of the altissimo register was that I often tried to capture higher overtones by biting more in my embouchure and blowing harder, when I needed to be utilizing throat positioning instead to reach higher overtones as well as to develop better control of them.

Check out these books for a much more comprehensive understanding of the altissimo register:

Top-Tones for the Saxophone: https://www.amazon.com/O2964-Top-Tones-Saxophone-Four-Octave-Range/dp/082582642X

Saxophone High Tones: https://www.amazon.com/Saxophone-High-Tones-Eugene-Rousseau/dp/158106005X/ref=pd_lpo_sbs_14_t_1?_encoding=UTF8&psc=1&refRID=T61FKP0VVR5H1CHJRB5W

Beginning Studies in the Altissimo Register: https://www.amazon.com/Saxophone-Beginning-studies-altissimo-register/dp/B00072ZF9C/ref=sr_1_1?s=books&ie=UTF8&qid=1505855702&sr=1-1&keywords=rosemary+lang+altissimo

There's a great book by Dr Rousseau that goes over some good fingerlings for all saxophones. Also there are some good exercise to get your embouchure like it should be in order to play altissimo. Here's the book - https://www.amazon.com/Saxophone-High-Tones-Eugene-Rousseau/dp/158106005X

Once you get comfortable with using the front fingerlings for E, F, and F#, you'll be able to seamlessly go to G.

Another possible friend: "Saxophone High Tones" by Dr. Eugene Rousseau.