From Skillmans of America:

b. 1635-40. Soldier under Col. Richard Nicolls in Expedition of Duke of York, ordered by the King, Feb. 25, 1664, sailed from Portsmouth, May 15, and dropped anchor in the harbor of Nieuw Amsterdam (near present Fort Hamilton [ed. Brooklyn, next to Verrazano Narrows Bridge]), Aug. 18, same year. After the surrender he stayed in this country and became “inhabitant and freeholder” at Newtown (L.I.), under Nicolls’ Patent of Jan. 23, 1666. Served in Esopus War; honorably discharged April 6, 1668. (See Introduction, ante). In 1669 he m. Sara, dau. of John Petit, Newtown, of whom Huntingdon (Hist. of Stamford) says: “John Petet was here (Stamford, Ct.) early, and had children recorded to him before 1650. Inventory, dated 5, 4, 1676, made by Richd. Law and Francis Bell, mentions his widow, Sarah (Scofield), two sons (names not given), and daus. Sarah, Mary, and Bethia. Richd. Law appointed guardian of his (John Petet’s) children in a court of magistrates, the Govr. being present, 14, 4, 1662. Debrow Pettit here (Stamford) in 1657. Name afterward spelled Petit.” Rev. Samuel Orcutt (Hist. of Stratford and Bridgeport, p. 103) says: “John Pettit was in Roxbury in 1639, and at Stratford in 1651. Probably soon removed to Stamford, and thence to Newtown, L.I.” John Petit and Sarah Scofield, his wife, were the parents of Sara, wife of Thomas Skillman.

I have a note that identifies two possible sets of parents for Thomas1:

Thomas and Alice of Oving in Buckinghamshire
Richard and Rose of Littlemore near Oxford.

Thomas Skillman and Sarah Pettit were married in 1669 in Stamford, Fairfield, CT. Sarah Pettit, daughter of Thomas Pettit and Christina Mellowes, was born about 1634 in Boston, Suffolk, MA. She was born about 1648 in Newtown(Maspeth Kills), Queens, NY. She died about 1704 at the age of 70 in Newtown(Maspeth Kills), Queens, NY. Sarah was buried about 1704 in Newtown(Maspeth Kills), Queens, NY. Of Dutch or Huguenot lineage

Thomas Skillman-22 and Sarah Pettit-23 had the following children:

Thomas2 Skillman II-18.
Elsje/Elsie Skillman-67.
Sarah Skillman-68.
Lijsbet/Elizabeth Skillman-69.