William Beekman parentage

I have been unable to trace the parentage of my 3x great-grandfather, William Beekman. He lived in New York City; was born about 1806-1807 and died September 1856. He was married in 1834 to Catharine Louisa Asten. He had six children: Emma (1835), Josephine (1836), William (1838), Clarence (Thomas, 1840), Adelaide (1845), Dudley (1847) - dates of birth approximate. The spouses of the children were: Emma to James M. Talman, Josephine to Joseph W. LaFetra, Clarence to Mary Mead, Adelaide to James M. La Coste, and Dudley to Frances Eldred, Mary Sayre and Agnes Vail.

Further research on this Beekman side of my family is stymied by this lack of information on his parentage. Any help or clues are most appreciated. Thank you, Kate Pecarovich.