Thank you contacting Ask Extension. If you would like to find an arborist in your area that could help you prune your semi dwarf apple tree you can go to the Trees are Good website and put in your zip code and it will give you a list of certified arborists in your area. If you decide you would like to try pruning it yourself, I have listed several good links to articles about pruning your apple tree. Your local Conservation District https://www.livingstoncd.org/ or MSU Extension Office https://www.canr.msu.edu/livingston/county-extension-office may offer some pruning instruction. I am not a MSU arborist, but here are some suggestions.

Since your apple tree is already 6 years old and should have been pruned once a year before this, you need to start identifying a central leader. You want to avoid excessive pruning all in one year, so I would suggest selecting two or three of the strongest, straightest of those branches growing upward (vertical) and prune all the other ones off this year.

Once your tree reaches 12-16 feet tall, for a semi-dwarf apple tree, you want to prune that main leader to promote side shoots and limit future growth.

Research tells us that a branch that grows straight up (vertical) produces mostly vegetative growth and very little fruit. Branches that grow straight out (horizontal) produce a lot of fruit but very little vegetative growth. Your pictures indicate very little horizontal branching. Selecting a central leader and cutting the top of that branch (heading cut) will help with that.

The upper branches (horizontal) must be kept shorter than the lower branches to prevent shading. The tree shape will roughly look like a Christmas tree.

The best time of year to prune is when the tree is dormant, January through April.

Avoid leaving long stubs when pruning, but don’t cut too close to the remaining branch either.

Use tools that made specifically for pruning and keep them sharp and clean.

Here are some links to great article with many good diagrams that will help you prune your apple tree properly to promote healthy growth and eventually produce apples.

https://www.canr.msu.edu/home_gardening/uploads/files/PruningApple-Pear_AA.pdf

https://www.canr.msu.edu/resources/smart-gardening-pruning-and-training-backyard-apple-and-pear-trees#:~:text=Repeat%20the%20process%20to%20make,to%20a%20weak%20side%20branch.

https://fruit.webhosting.cals.wisc.edu/wp-content/uploads/sites/36/2011/06/Training-and-Pruning-Apple-Trees-1.pdf

https://extension.umn.edu/growing-apples/pruning-and-training-apple-trees