ASAP stands for Atypical Small Acinar Proliferation. ASAP diagnosis is usually related to cells that do not classify to benign neither malignant but to a probably of both.
In some studies pathologists have found that high PSA in ASAP presence, lead usually to adenocarcinoma classification later. In any case you will have to repeat the biopsy to get a confirmation.
I wonder what made you to get a Saturation biopsy. Usually that is done when the traditional 12 cores is negative to cancer but the PSA is high. Can you share more info on your case?
The good thing in the results is that ASAP was found only in three cores which indicate a small volume of this type of cells. If they turn out to be malignant your case would be the typical low risk to which Active Surveillance is recommended.
This regimen of continuous testing may in fact be what you have been done up to now.
For peace of mind you could get a second opinion on the samples from a laboratory like Johns Hopkins or Bostwick.