Please see my web page that will answer many of your questions. Follow the links to the Solomon Phipps family pages. You will find an Asa Phipps recorded as the son of a Samuel Phipps of Lisle, NY. I have nothing on his descendants. To my knowledge, it has not been proven that this Asa was the same Asa as ASA K. Phipps, your ancestor. It makes sense that it is the same person, but definite proof is lacking at this point. The Asa in Lisle was descended from Solomon Phipps (b. 1619) who came to Charlestown, MA in the 1630s or 1640s from England. About that same time, James Phips (b. @1610) settled in Maine from Bristol, England. Solomon and James had different parentage and were from different parts of England. They could possibly have been cousins, but that has never been proven. James Phips was the father of Sir William. Sir William had no biological descendants, but had an adopted son Spencer who was the nephew of his wife. Spencer's family is well documented and were loyalists during the Revolutionary War, returning to England during that time. My own family also claimed we were 'descended from Sir William', when in fact we were descended from his brother John. I have the family of James Phips well documented on the web pages.
The families of James, Solomon, Spencer and Asa K. are all shown on my web pages and can be found by following various links. I have studied this family for 25+ years and have a lot of information on these early lines. Still, have found no connection between Solomon and James, the two earliest Phipps settlers in New England. Many families latch on to Sir William as their 'ancestor', but the fact is, he had no descendants. Hope this has helped. Let me know if you have further questions. I am happy to help out if I can.