My family has maintenanced A lot Which we have used as our Backyard for more than 44 years. The property owner of the house next door to us went behind our backs and purchased the lot, and without knowledge of this my family stilled maintained up keep of what we thought to be as our Backyard. My question is : Can my family begin an Adverse Possession Case Against this Property Owner?
No. Since you thought the property belongned to you it was not adverse to the owner. Therefore you have no grounds for adverse possession based on the facts as you have described them.