No. As I understand it, Timothy Winslow, of Perquimans District is not confirmed as a son of Joseph Winslow
There’s a Will of Joseph d 1679 on file in NY that could be consulted.
https://www.pinterest.com/pin/joseph-winslow-16361679-framed-will-o...
Found more information.
No proof was found that Joseph Winslow was the father of Timothy Winslow, of Perquimans District of age in Perquimans County NC in 1702 and founder there of a family. Although Joseph Winslow was asked to serve as foreman of a jury 1677-8 in Perquimans Co. NC, he is called "another New England traider" in the NC COL REC, which thus does not prove he owned land or resided there.[1]
https://www.familysearch.org/tree/person/details/L64S-ZGT
Timothy is NOT Joseph's son, according to DNA analysis. In fact, Timothy is not a direct descendant of Kenelm (born 1599) Winslow at all. Here is an article about this data:
DNA Findings for Kenelm, Timothy, Thomas and John-2005
“The Winslow Family Y-DNA Project, that was started in April of this year to help all branches of the Winslow family identify their origins, has made significant advances in the past six months.
“A number of Kenelm (b.1599) descendants who participated in the project laid the groundwork for the New England Winslow DNA fingerprint. We now know 24 to 25 of the 26 DNA markers for Kenelm, for a better than 90% confidence for his fingerprint. This will allow any potential descendant, desiring to confirm Kenelm as an ancestor, the opportunity with a quick DNA test either directly if they are a male Winslow or indirectly through a surrogate family member who is.
“Most recently, significant results have culminated for the Southern Winslows in the DNA fingerprint for Timothy Winslow (born about 1654). With only three descendants of Timothy we have a 99% confidence of Timothy's DNA fingerprint. Additionally, the results have confirmed that believed sons Thomas (born 1682) and John (born 1699) are truly brothers. This was a unique situation where two descendants of Thomas and one of John all have all 26 DNA markers exactly matching, allowing the high confidence for the DNA fingerprint.
“The connection between the Southern and the New England Winslows are not yet fully conclusive. There are enough DNA markers in common to know that there is a related connection between the two branches. However, the DNA genetic distance is such that it is very doubtful the common ancestor occurred as early as Edward Sr. (born 1560).
“The project is actively searching for any male Winslow descendants of John Winslow (born 1597) and of course any of those of his sons or brothers. Finding a direct male descendant of John Winslow could be the keystone to finalizing Kenelm's DNA and confirming the Southern and New England connection.
“Again, anyone who wishes to confirm their ancestry to either of these branches of the family may either have their DNA tested, if they are a male with a Winslow surname, or use a family member who is as a surrogate and have a high confidence in a conclusive outcome.
“For more information on the Winslow Family Y-DNA Project, registration process or DNA questions in general, you can access the project's website.