On May1, 1862 the 3rd NY Cavalry are somewhere between Haughton's Mills April 27 and near Burnt Church May 7. May 1, 1863 the 3rd NY Cavalry are in an expedition toward Kinston April 27-May 1 (Detachment), Wise's Cross Roads and Dover Road April 28, near Core Creck April 2, Core Creek April 30, and Evans' Mills May 5. The reference to 90 men, "about ninty men of the 3rd NY Cavailry had A running fight with about three hundred Georga Cavilry," might be the detachment in Kinston.

The signature is "Brother, Harrison".

I found 6 Harrisons with NY Light Artillery:

Harrison Balcom 23rd Independent Battery, New York Light Artillery
Harrison Miller 6th Independent Battery, New York Light Artillery
Harrison Prescott 4th Independent Battery, New York Light Artillery
Harrison B. Range 1st Independent Battery, New York Light Artillery
Harrison Smith 1st Independent Battery, New York Light Artillery
Harrison Terry 7th Independent Battery, New York Light Artillery

Someone could lookup these batteries up in the NPS system to see which may have been in the same area on the May 1, 1862 or 1863 dates.

The other thing to consider is that the soldier may have written the wrong day or date.

Ed