For the Presidency ? Whomever would be the highest duly-elected officeholder as of January 20th. The Speaker of the House would be acting President in this instance.
However, this is something I’d see more likely as happening in a Governor’s race if anything, with either the Lt Governor/Sec of State/Atty Gen or legislative leader serving in an acting capacity.
When they had a situation in Minnesota in 1963 with a hung election between incumbent leftist RINO Gov. Elmer L. Andersen and Democrat Lt. Gov. Karl Rolvaag, Andersen remained a few months past the end of his term after the election was certified (he lost by 91 votes).