With the fading of the Federalist party in many areas and the lack of organized political "parties" in the modern-sense, several candidates for election were often described in terms of their support for a single candidate.
New York 1806-08: Morgan Lewis was the Governor of New York from 1804-07. He was elected in 1804 with the support of DeWitt Clinton, but after their split, those supporters of Lewis would be described as such in many newspapers.
Pennsylvania 1805, 1811: With the split in the Republican Party in Pennsylvania in 1805 (See
"A strong and aggressive Federalist Party had contributed much to the Republican victory in Pennsylvania in 1799. It had forged Republican unity and, by its excesses, had added large numbers to the ranks of its opponents. After the election of 1800 Federalism in the State declined precipitately; and within two years John Quincy Adams was to describe it as 'so completely palsied, that scarcely a trace of it is to be discovered except in here and there a newspaper edited by New England men.' (ft: John Quincy Adams to Rufus King, October 8, 1802 in Charles R. King (ed.) The Life and Correspondence of Rufus King, 6 vols. (New York, 1894-1900), IV, 176.) Gratifying as such a metamorphosis must have been to the Republicans, it was not without its cost. The virtual disappearance of Federalism weakened the compulsion for unity and gave play to Republican differences on measures and men which by 1802 had resulted in a number of local divisions in the party." (The Keystone in the Democratic Arch: Pennsylvania Politics, 1800-1816. Sanford W. Higginbotham. 1952. p 25)
"Whatever the true explanation of these intricate political maneuvers, the  senatorial election had disclosed division in the Republican ranks. The party had begun a new era in its history." (Higginbotham, p 34)
Pennsylvania 1808, 1813-14: Michael Leib was elected in 1808 as a U.S. Senator from Pennsylvania. In that same year, Thomas Humphreys, a candidate for the Bank Director of the Bank of Philadelphia was described by The True American as "Leib's candidate." Later, in 1813 and 1814, factions would develop in the Republican Party and many candidates for elections in these two years would be described by The Democratic Press (Philadelphia) as Leibites.
Much of the division in Pennsylvania, and specifically, Philadelphia politics stemmed from those supporters of Simon Snyder, who was the Speaker of the House, and later Governor, and Michael Leib, whose power over the Republican party lead to the Constitutionalists, those supporters of then governor Thomas McKean, to split away from the Republican Party in Pennsylvania as a whole and form their own party for several years, from 1805-1808.
"The new era was dominated by two themes. The first of these was the national issue of supporting the administration's foreign policy, including the War of 1812. Party lines were sharply drawn, and a strong Federalist minority took an active part in politics. The second was the bitter feud between the Leib-Duane faction and the followers of Snyder. This persisted in full rancor throughout the period and was only partially subdued by the compulsion for the Democratic unity exerted by the War of 1812." (Higginbotham, p 177
"The second period, which ended with the election of 1808, was characterized by two main questions - whether the Federalist-Quid coalition was to form the basis of a permanent new party; and whether the city Democrats, led by Leib and Duane, or the country Democrats, controlled by the adherents of Snyder, should dominate the party. The growing importance of foreign relations arising out of American neutrality in the Napoleonic wars settled the first question in the negative and forced the postponement of a decision of the second. In the face of a resurgent Federalism, Pennsylvania Republicans suppressed their differences and united in a successful support of Snyder, Madison, and the embargo. Foreign affairs continued to be important for the next three years; but congressional vacillation and the relaxing of Federalist efforts within the State permitted the Snyderites and the Duane-Leib faction, now known as the Old School, to fight out their battle for control of the party. The Olmsted affair offered the occasion, and for a time it appeared that the Old School might be victorious. However, its own intemperate violence and political blundering redounded to the benefit of the Governor adn his adherents; and by 1811 Duane had forsworn State politics, and the Old School consisted only of Leib and a few hangers-on. The Snyderites not only dominated the State as a whole, but, acting through Binns, had achieved supremacy in Philadelphia." (Higginbotham, p 328-329.
Pennsylvania 1819 Speaker of the House: Joseph Lawrence is listed as a Findlayite. In the same election, Rees Hill is listed as a Binnsman by the American Republican of December 14, 1819 and as a Binnite by the Crawford Weekly Messenger (Meadville) of December 17, 1819. The Village Record of December 15, 1819 lists Lawrence as an Administration candidate and Hill as an Anti-Administration candidate.