You should make the cut where I have drawn. You can either use some bypass loppers or a pruning saw. You can also use a regular cross cut hand saw if that is all you have. If you use loppers, be very careful to not cut into the branch you want to keep. This means you will need to cut out near the tip of the cutter, and that in turn means the force you will have to apply to the loppers will be high. I can't really tell how large diameter that branch is but based on the webbing, I am guessing 3/4 inch to an inch. I would probably use a saw. One trick is to cut the branch off maybe a foot farther away than you want the final cut, and then cut it again where you really want the cut. Doing that lets you get most of the weight off and if the bark peels off some on the first cut, it won't matter. Then when you make the second cut it is easier to get a really clean cut because the saw won't bind and the falling branch wont tear any bark. You are going to need to cut from the low outside of that crotch in and up for the final cut.
If you have a pruning saw, use it. You pull that towards you to cut and it is a lot easier than a regular cross cut hand saw.
In the future, try not to let two branches grow with such a small angle in the crotch. It makes for very weak crotches and when the branches get large, they can even push against each other and the crotch can split.
The best thing is when new branches start, you can tie them with strings to stakes or other branches to get them to grow in the direction you want.
Looking at that tree, a lot of the branches look too long and spindly. I would cut maybe a quarter to a third from the more spindly ones. That will also help the trunk and roots grow more and make the tree more sturdy.
Lastly, that tree is planted very close to the fence. You should not let the tree grow very large on the side opposite the fence or it will not be balanced over the trunk and roots. You are going to need to grow the tree with a fan shape. wide along the fence and narrow going towards and away from the fence.
Look up "espalier apple" You don't have to go to that extreme, but maybe halfway between a round tree and the espalier would work. There are not a lot of absolutes.
The main thing is have fun and enjoy the apples when it starts to produce.
