I have learnt to start harvest the Jujube once some of them turn reddish. They are ripe and sweet even if they are green in color.
The Jujube plants tend to send out many suckers or water sprouts. They tend to be more thorny that the variety plant we purchase. If you look at the picture below, you see the larger fruits on the left. On the right are tinier and more fruitful branches of the sucker branches. I am greedy. If I had missed trimming off the sucker earlier in the season, I leave the suckers to keep growing and enjoy the fruits.