Greetings Sloth,
Yes, oddly there were two 1st NY Artillery Batteries with the B designation.
Pettit’s Battery 1st Regiment, NY Light Artillery which was in the II Corps 1st Division.
Pettit’s Battery came from Chemung, & Onondaga counties and mustered Aug 30, 1861.
Equipped with six (6) 10 pound Parrotts.
But there was also a 1st Battalion NY Light Artillery which consisted of four batteries and was mustered in New York City.
1. Battery A under Wever, mustered Aug 26 1861, equipped with four (4) 20 pound Parrotts.
2. Battery B under Von Kleiser, mustered Aug 12 1861, equipped with four (4) 20 pound Parrotts.
3. Battery C under Langner, mustered Sept 11 1861, equipped with four (4) 20 pound Parrotts.
4. Battery D under Kusserow, mustered Sept 20 1861, equipped with six (6) 32 pound Howitzers.
This Battalion was part of the Artillery Reserve and was attached to the V Corps, and under Commander of the Artillery Reserve Lt. Col. William Hays.
As to why Battery B for the 1st Battalion isn’t listed the same as the others, I believe it was created long before the identification modifications were implemented in the tool.