Here is how I usually play altissimo G#, A and Bb on the saxophone using what’s sometimes known as the triangle fingerings. The right hand forms the triangle with Ta (side Bb), Tc (side C) and 4 (F). The left hand simply fingers 1,2 and 3, like a high G, with the octave key of course.
For altissimo A you raise the first finger on the left hand, so you’re just using 2 and 3. Right hand stays the same as before.
For altissimo Bb you raise the second finger on the left as well, leaving only finger 3 down. Right hand stays the same again.
The three fingerings are very similar, they’re relatively easy to produce, stable, in tune and allow for easy movement between them. If your setup is too soft then altissimo will be difficult, so adjust the reed as necessary. Don’t worry if you get is a lower (or higher) sound, it takes quite a bit of practice but you will find it improves your tone and control over the instrument over time. Do also check out this video on how to play altissimo G:
https://www.youtube.com/watch?v=HL3ORyunWPw