Prior to July 16, 1990
Roman line: John XXIII-II, Paul VI, John Paul I, John Paul II the Great Deceiver, Benedict XVI, Francis
Mysticalists, claiming an alleged apparition: Gregory XVII, Clemente Dominguez, 1978-2005, Clement XV, Michal Collin, who resigned in favor of Gregory XVII, Gaston Tremblay
Non-Catholic: Pope Peter II, Chester Olszewski of Pennsylvania, a former Episcopalian priest, who asserted his claim in 1978.
Consideration of the claim that Joseph Cardinal Siri was elected Pope.
The balance are internet fictions, made up. Of these, no information can be found verifying that they even truly exist, much less asserted a claim to the papacy.
The Wikipedia article on Conclavism lists a number of alleged claimants. Those that are not internet fictions come long after the 1990 election. No one ever addressed the 1990 election, although it is certain that the 1994 and 1998 elections listed below knew of the 1990 election.
There were three lines subsequent to July 16, 1990.
Linus II, Victor Von Pentz elected in Assisi Italy in 1994 by several Traditionalist priest and bishops, some of whom were aware of the July 16, 1990 election. Von Pentz has faded into the wood work. Last rumor places him as a bank guard in northern England.
Pius XIII, Earl Lucien Pulvermacher, elected by several Traditionalist lay people in a phone in election. Pulvermacher was a Traditionalist priest, brother of Father Carl Pulvermacher. He was elected in 1998 and died in 2009. No one has been elected to succeed him. He was well aware of the July 16, 1990 election.
The last group had a line of three, the last resigning into a vacuum. Pope Leo XIV (2006-2007). On 24 March 2006 a group of 34 episcopi vagantes elected the Argentine Oscar Michaelli as Pope Leo XIV. On his death on 14 February 2007, he was succeeded by Juan Bautista Bonetti, who took the name of Pope Innocent XIV, but resigned on 29 May 2007. He was succeeded by Alejandro Tomás Greico, who took the name of Pope Alexander IX.