There were 2 James Rankins, father and son. Neither was killed at Oriskany.
The following is about the younger:
From Rev. War Pension Application #S14255 of James Rankin
That he served as a common soldier in Captain Damewood's company until late in the fall of the year 1776, when he, with several others were drafted out of said company and were dispatched to Stone Arabia where they were joined to a company of rangers of which Christian Getman was Captain belonging to the same regiment. Nicholas VanAlstyne and Laurence Gross were the other officers of this company of rangers, but he cannot state their particulars of office. With this company he went in the winter of the years 1776 and 1777 to build a bridge across the stream at Tyconderoga to Mount Independence to prevent the enemy from passing with their shipping and munitions of war. That he worked for a long time at this bridge, it was called a sinking or floating bridge and was under the surface of the water, but he cannot recollect whether the bridge was completed, but of one fact he is certain, it was a cold job, and in the prosecution of it he endured great fatigue, suffered from hunger and want of clothing. That when he and his company left Tyconderoga, which occured in the latter part of the winter of the years 1776 and 1777. They were ordered, he believes, to Albany, and when they arrived on this journey, to a place called Saboda Point on Lake George about midway between Fort George and Tyconderoga, they were surprised and attacked by a band of Indians and Canadians commanded by one Captain McCoy: an engagement ensued and Rankins and about 25 or 30 others were taken prisoners and four others killed and the remainder of the company escaped. Rankins and the other prisoners were taken to Montreal, and in performing that journey at that season, suffered extremely from fatigue and want of food and of the number one perished on the way. He (Rankins) was for a long time (he cannot state the length of time) confined in prison in Montreal and until an exchange of prisoners took place, he did not get an opportunity to escape, being closely watched and remained in Canada until the close of the war.
Rankin, James Jr. Priv. Capt. Marc Demout's Rangers [THIRD TRYON COUNTY REGIMENT], from March 15, 1777 to May 21, 1783. --"CASUALTIES, Prisoners From the Militia," in Berthold Fernow, ed., Documents Relating to The Colonial History of the State of New York Volume XV. State Archives, Vol. I; Albany NY: Wood Parsons and Company, Printers, 1887.
"Saboda" is Sabbathday Point, Lake George, where a number of persons of different units were captured on March 19-20, 1777, by a British scouting party. The British records say he was a “young lad” from the Mohawk R., was born in Scotland. Said he was forced to enlist in place of his father, to go to Ticonderoga; said he wished to stay in Canada, and was left at Montreal in May instead of being put on a prison ship. One British record states he was of the 1st NY (VanSchaick), but the man by this name on the rolls of Capt. Finck’s Co. was not among those sent to Ft. George, and was mustered as present into 1778. The captive may be the James, Jr., of Capt. Marc Demouth’s Co., 3rd Tryon Co. Militia, listed as a prisoner by Fernow.