The only good candidate in the 1910 Onderdonk genealogy is
138 Adrian Onderdonk (Rem, Adrian, Andries, Adrian, Andries) was b. June 22, 1788, at Clarkstown, Rockland Co., N. Y.
Thomas, m., had daughters. Col. Benjamin T., m., had one son, Col. Benjamin, lived in Plainfield, N.J.
That's not much to go on and the line in the book stops right there.The birth date is about right though as are the names and he did seem to get to New Jersey.The letter T is definitely not F, although I've found it is extremely easy to get them mixed up reading old handwriting.It would hardly be the first time the Onderdonk genealogy had middle initials wrong.My great grandfather's middle initial is incorrect in the book and I've seen some names pretty garbled or completely wrong from what might have been misread handwriting.
If this is your message from another forum
"Am looking for any information concerning the 1st New York Mounted Rifles. Husband's grandfather Col Benjamin F. Onderdonk demoted himself from the 5th NY Volunteers to go to this regiment. Have lots of info from 5th NY Volunteers. But cannot find much on the 1st NY M.R. Can anyone help?"
then I've got to believe this is the right Adrian Onderdonk.If it is the right one, documenting it is another matter.However, you can probably try to get the older Benjamin Onderdonk's military service and/or pension records from the NARA.That might clear things up.I'm trying to get my great-great-grandfather Andrew S. Onderdonk's records now.The paperwork has gone in, now I'm waiting.