Here is the Covington Journal's post battle coverage of the Battle of Mill Springs. The battle took place on January 19, 1862 and this article is from January 25. I've seen it called "Logan's Cross-Roads" before, but this is the first reference to the "Battle of Somerset" I have seen.
Battle of Somerset
Defeat of the Confederates
Death of Zollicoffer
On Sunday morning, Jan. 19, at 6 o'clock, Gen. Zollicoffer, with a Confederate force, said to have numbered nearly 10,000 attack (sic) the Federal forces, under Gen. Thomas, near Somerset. The battle raged with great fury until the middle of the day, when the Confederates gave way and retreated to their intrenchments near Mill Spring. Gen. Thomas pursued them, reaching the foot of the hills just at night-fall, where he bivouacked, intending to attack the Confederates the next morning. During the night, however, the Confederates withdrew across the river, leaving behind their artillery, wagons, ammunitions, horses, &c., but destroying most of the boats in which they crossed the river.
Gen. Zollicoffer was killed, it is said, by Col. S.S. Fry, of the Fourth Kentucky regiment, and his body found on the field. The rebel loss, besides Gen. Zollicoffer, is stated as 114 killed, 116 wounded and 45 prisoners not wounded. The Federal loss was 39 killed and 150 wounded. They captured 14 cannon and 1,400 horses and mules.
The Federal force is not given. General Thomas was reinforced Saturday night by Gen. Manson's brigade, numbering four or five thousand, and during the engagement by the Tenth and Twelfth Kentucky, First and Second Tennessee, Fourteenth, Thirty-first, Thirty-fifth and Thirty-eighth Ohio, and by Standart's, Whetmore's and Kenney's batteries. The Confederates had 16 cannon and the Federals 22.