Robert, the year would be 1884. These bar action locks were first patented by Alexander Brown November 27, 1883. It is very possible this type of hammer gun was made then but I think it started in early 1884. There are no records for these guns. The patent date of June 1-80 is the only patent that Baker had and that was for the "J" spring that holds the for-end on.
Your gun with Stub Twist barrels would be a Quality F, the lowest priced hammer gun. Cost was $50.00, a good sum of money then when laborers were making a $1.00 a day.