Looks like infested by apple maggots. You can spry, bag each apple or cover branches with row cover.

So I take it that lime sulphur spray that I have applied in the fall and spring for the past 3 years does not combat "apple maggots"?

What spray does one need to combat this pest?

(Remember this is just one tree on residential property)

May I suggest that if you want ready-made answers from previous posts, please google:Garden web forum, apple maggots.

Many old posts will show up for you to read. Most of the times, someone knowledgeable have given answers in those old posts. You'll learn a lot in a short time.

You need to learn not only what to spray, but when. This is a summer pest.