Those are aerial burr knots, where the rootstock is trying to sprout roots. Some rootstocks are more prone to this than others, and the strategy is to bury the rootstock as deep as possible. It will stunt the tree's growth, and there's nothing you can do for it.

It may be that the scion (top part of the tree that was grafted to the rootstock) died out long ago and that your whole tree is a rootstock. I'd pull it out and plant a good variety that you like, as this one's days are numbered.

Applenut