Question
Last spring I planted a dwarf peach tree. few weeks later it had new growth on the side. This growth had green leaves and not the purple ones. This year those are coming back green. Is this normal?

Also, how can I encourage growth to the original part of the tree?

Answer
I hope I understand what you are saying. The Patio Peach tree is a "graphed" tree. This means that a small version of the regular size tree is graphed on to larger tree. If the green leaves are coming on the bottom portion, and not the top dwarf graphed portion of the tree, then this presents a problem. It could mean that the graph is not "holding" well, and it is sending all of the growth energy to the bottom and not the top.
I would first try to focus the growth energy to the top of the tree by cutting all growth around the bottom of the tree below the graph. Then prune back the top portion to a leaf node. ( Just above a leaf bump) This will encourage new growth from this part of the limb. As you do this be aware of the shape of the tree. Make the cuts as even as you can so that the tree is not unattractive. I would do this as soon as possible. You want to encourage spring growth when it comes out of dormancy. When the weather warms and it has full new leaves, give it some fertilizer to encourage still more growth. But keep the lower area below the graph clean at all times of any growth.