New York State Model Carbine

[Brant6]

Recently I purchased a Remington Rolling Block. There are few markings on the firearm itself and no visible serial numbers or caliber identification. The information I have gathered indicates that this is a New York State Carbine Model. I base this on the patent dates and barrel length. The stats on the firearm is as follows:

Overall Length: 38 ¾”
Barrel Length: 22”
Calibre: 50-70 Gov
Type of Action: Rolling Block

The only stamping on the firearm are the patent dates and an “S” on the left forward side of the receiver. There is a “U” on the forward stock retaining ring which I understand is for proper installation. The patent dates are as follows:

REMINGTONS . ILION. N.Y. U.S.A.
PAT MAY 3D NOV 15TH 1864 APRIL. 17TH 1868
AUG 27TH 1867 NOV 7TH 1871

I have read that there may be stamping located under the barrel at the forward end of the receiver and just above the trigger guard. I have not removed the stock. Would such markings exist?

I am trying to gather provenance on the firearm. Were any of these firearms exported to Canada? Any information provided would be appreciated.