If so, what were they and who were their leaders?
James McPherson, Battle Cry of Freedom, covers it in some pages at the start of chapter 23, "When This Cruel War Is Over".
Formal political parties did not exist in the Confederacy. This state of affairs arose from two main causes: the erosion of the two-party system in the 1850s and the perceived need for a united front during the emergencies of secession and war. ... the most assiduous researchers have been unable to identify party organizations or significant partisan patterns of voting in the Confederate Congress from 1861 through 1863.
"Southerners considered this circumstance a source of strength." McPherson (following Eric L. McKitrick, "Party Politics and the Union and Confederate War Efforts") disagrees. In the North, parties could channel support or opposition, and people by voting could register agreement or disagreement. Also, government members of all levels who were Republicans were bound to support of the war effort; in the South "the centifugal tendencies of state's rights were not restrained by the centripedal force of party". Also, the Confed Constitution limited the president to a single six-year term, "so Davis had no reason to create a party organization for re-election".
But "Historians have identified 'proto-parties' emerging in the Confederacy by 1863", with people he identifies as being "opposition" to Davis emerging in the 1863 elections: either they demanded peace through negotiations (but not so many), or they backed the war aims but not the means or the governmental people.
Being McPherson, he provides plenty of sources in footnotes.
I answered that a few weeks ago here.
Essentially, that's a no. There weren't formal political parties in the Confederate government. That doesn't mean there weren't factions of course. Check out the atlas by Martis and Pauer that I linked to for more there.