Hello
@Jclynn911 and welcome to CivilWarTalk - the best place on the internet for Civil War discussion. You've come to the right place! I can help with interpreting some of the information from the register and I'm sure there are others who will be able to help with finding the Hospital records from Philadelphia for November 1862.
On August 18, 1862, at age 24,
John J. Vanderbogart enlisted as a Private into the 120th New York Infantry at Kingston, for three years. He was mustered into service on August 22, 1862 and assigned to Company I, 120th New York Infantry. He was noted on the Company Muster Roll as absent in the hospital at Philadelphia November 1, 1862 (to April 10, 1863?)
He was listed as present on the Company Muster Roll as of April 30, 1863 [meaning he had returned to his regiment.] The Company Muster rolls show him absent, serving in
Battery K, 4th US Artillery December 31, 1863 through April 30, 1865. [So even though he enlisted in the 120th New York, he served most of the war in Battery K, 4th US Artillery.] The last notation in that row of dates says he was absent sick in Genl. Hospital, probably at the time the April 30, 1865 Company Muster Roll was completed.
Underneath that, it notes that John J. Vanderbogart was born in Woodstock, NY. At the time of his enlistment, he was 24 years old and, by occupation, a farmer. He had grey eyes, brown hair, a light complexion, and was 5 feet 8 1/2 inches tall.
Back near the top, under "Left the Organization" the notes indicate that he was discharged in 1865 [date not give] under General Orders No. 77 and that "No discharge was furnished." [I don't know what General Orders No. 77 said, but someone else will likely be along who does.]
Again, welcome to CivilWarTalk. Happy to have you aboard.
EDIT TO ADD: Looks like your John J Vanderbogart may have also served in Company C, 20th New York State Militia 100 Days 1861. The 20th Regiment, New York State Militia (100 days, 1861) was organized for three months' service April 23, 1861. The regiment mustered out August 2, 1861.