New York, April 4. —A letter to the Cincinnati Gazette, gives some particulars of the recent fight near Somerset, Ky. The rebels were overtaken four miles north of Somerset. Gen. Carter in command of eight hundred mounted men, had reached Buck Creek, when Gen. Gilmore, with his body guard, and the seventh Ohio cavalry reached him, increasing our force to twelve hundred. Skirmishing then commenced at Button’s Hill, twelve miles from Somerset. The rebels took up a strong position, and planted batteries. It was about noon. An artillery fight began, and lasted about an hour and a half. We dismounted three of the rebel guns. The wings were then ordered to advance. Wolford on the right, did so, and he was wounded.