Am looking for the parents of the Beletje Quick/Kwik who baptized a son named Solomon in the Kingston RDC: 11 Sep 1709 at Kingston: [Hoes B#1772]  [Father not named], Beelitje Kwik; Salomon (Illegitimate); Wit: Hendrik Dekker, Claartje de Hooges. This Solomon married Lea Decker, dau of Jacob Jans Decker and Antje Hendricks Kortreght. And, either the same Beletje or another Beletje Quick/Kwik who also baptised an Illegitimate son named Joel in the KRDC: 1726 Jan 16; , Beeletjen Kwik; Joel (ill); Jury Best, Antjen Donsbeggen. This Joel Quick married Christina Middagh in the Machackemack RDC September 03, 1751. Both Joel and Solomon Quick named a daughter Beletje. Any clues would be greatly appreciated.

I consulted the Quick genealogy and think I have found a candidate.
"C11 Belitje Jacobs Quick (B2), was named for her grandmother.  She m. 1st Gerrit Cosyn (Cosine); 2nd, Theunis Jansze, "a widower from the Bay," banns pub. 19 Dec. 1706; m. 16 Jan. 1707 (Flatbush D.C., p.96).  The Will of Gerritt of Cozynse of N.Y., 7 Sept. 1702, mentions wife, Beeltie, and names "Theunis Quick, my brother-in-law, as Guardian of my children" (NYW 2:16)." (1)
1) Quick, Arthur Craig; A Genealogy of the Quick Family p. 22

The two children you list are given by the Quick genealogy as children of Elletje Quick.
"His name does not appear again in ch. records of Kingston, Wawarsing, Minisink or Smithfield.  A "Solomon Quick, member of United Empire Loyalists (A Tory Organization), Niagara, H District, wife and one child" (Provision List, Niagara, 1786)." (1)
1) Quick Genealogy p. 41

"D 52 Joel Quick (C36) , bap. 16 Jan 1726 (Kingston, Ulster Co. Birth Records:3430).  Wit.: Jury Best and Antjen Donbeggen.  "Joel, y.m., m 3 Sept 1751 to Christina Middagh, y.w. (Minnisink Church Records:26 Records show that both resided at Machackemeck (Port Jervis).  Banns registered 3 July 1751."

"C36 Elletje Quick (B5), bap. 21 July 1688 (K68, m a Quick; had 2 children (D51-2)." (1)

I am in possession of a Middaugh geneology dating back to Teunis Gijsbertssen Middagh, born about 1620 in Holland, emigrating to America at about age 20. There is a fairly detailed listing of descendants (names and dates of birth). In the sixth generation appears a Hendrick Cortright "Case" Middaugh (apparently the first to use this spelling), born 1754 Sussex County, NJ, married Jennetje Van Aken, Machackemeck, Orange, NY. One of his 11 children was Sarah Middagh who married a Daniel Quick, Westfall Township,PA. Any info on this particular Quick or any Middaughs of this time frame would be appreciated.