I would toss it, unfortunately. Especially if it was to be a gift.
The mold has "roots" that go much deeper than what you can see. It's possible for that to create an "off" flavor even if recooked. Yes, I've scraped mold off stuff and eaten myself, but I would never think of giving it to someone else.

Do all of your jars have mold?
Was it sealed properly?

You don't get mold without air in the jar somehow.
It sounds like the seal has been compromised at some point, either from improper processing or storage, or something bumped it hard enough to break the seal.

Deanna

You need to dump them all if this jar was sealed and so are the rest. It would most likely be in all the jars of that batch if that is the case. Mold has mycotoxins. It is linked to some kinds of cancers and arthritic conditions. Never eat anything with mold other than cheese that is supposed to have a healthy type of mold. What you are seeing is just the tip of an iceberg. The whole food is full of mold. Bread is the same way, any food that shows signs of mold. It is spoiled food.
Did you have it at a full boil when it went into the jars ? Did you properly can them in a boiling water bath canner ?
Did you use the right size of jar that is called for and not a larger jar ?

I opened some apple butter from last year and it was dark on top. What would cause that, and is it safe to eat?

It *probably* darkened from a little too much headspace in the jar, so the apples oxidized (just like they get brown when cut and left out on the counter). If you don't detect any mold and it smells fine, it's safe to eat.