I had this tree for many years and this is the first time seeing white soft mushy stuff on my tree. At first I thought it might be some kind of insect but it doesn't move when I smeared it against something else. I'm not sure what this is or if it's okay to just leave it.
Photos are somewhat blurry but it looks like a scale infestation: Scale Management Guidelines--UC IPM
That looks like the Cottony Camelia Scale that has been infesting my Kiwi vines for the last couple of years. It results in black Sooty Mold on leaves, stems, and adjacent structures. The Sooty Mold feeds on the honeydew secreted by the scale insects.
It seems like scales after looking up some pictures. It's only on one tiny branch right now so would just cutting off the branch work?
The cottony scale insects are easy to crush; I've removed hundreds of them from my Kiwi vines. So, you could just kill them and save the branch, but cutting off the branch will certainly work. However, the white things are just the egg cases of adult females. There could be immature scale insects on other parts of the tree; they are less obvious and easily overlooked. The white egg cases have just recently appeared on my plants. There may be more immature females that will develop eggs later; continued vigilance is advisable.