I am writing a creative story including a general from the civil war (I haven’t decided which) and I wanted to twist history. What battle could have saved the Confederate cause? I was thinking Vicksburg would have been a good battle, but I wanted to know if there was a more important battle that would have give the Confederates more of a chance. Thanks for the help. 
Might I gently suggest that you not attempt to write a story about a subject that you are ignorant of?
That said, the Confederacy never had a chance. It was only ever a matter of how long it took them to lose, not if they lost.
Once it kicked off it was inevitable the South would lose. This is my VOTE for possible alternate timeline Rebel victory. Capturing Washington was indeed possible early. I believe Ambrose Burnside had a great deal to do with keeping the rail line intact, as well as Lincoln for suspending Habeas Corpus on sabetuers.
Anyone writing Alternate History really needs to know their History. Or you could refer to any of the numerous If The South Had Won stories already written. (Sometimes, aliens help!)
As already noted, changing the results of one battle would not have sufficed.
An overwhelming, lopsided victory at Gettysburg *might *have done it. But several more Confederate victories would still have been needed.
Other than some incredible victory vs Washington DC in the first months, I can see one thing: the RMS Trent refusing to stop or even fighting back, being sunk- and Great Britain joining the war on the side of the CSA. Highly doubtful.
I think that this might be what I was looking for. Thank you very much.
Was Gettysburg where Lee insisted that a position be taken-“It vexes me”-and caused the battle to be lost?
The city of Washington was under serious threat for a surprisingly long time early in the war. Not much would have had to be different to posit its fall to the CSA, and a Northern reaction of “Let 'em have it, let 'em leave”.
But yeah, as long as the North *wanted *to win, they were always going to.
No battle could have saved the traitors. Doomed from the start, and damned for eternity.
They must have been some tough guys to go up against those odds and last that long. 
If either Antietam or the Atlanta campaign had been solid Confederate victories, then British intervention or McClellan’s election, respectively, would have been possibilities.
I don’t see any one battle doing it.It would take a sustained pattern of holding on long enough for the Union to get sufficiently war-weary to elect McClellan in 1864, which would be very difficult if not impossible for basic logistical/economic reasons.
I’m going to say Antietam was the Confederates’ best chance.
As others have said, there was never a time in the war when the Confederates had a real advantage. So basically, the Confederates needed a psychological victory to make the United States decide that the war wasn’t worth fighting.
The only way for the South to win would be for the North to capitulate. There was no way that the South to win an outright military victory. So, I’d go with Gettysburg…if the South had completely crushed the Union Army at Gettysburg and then been able to drive on to surround or even seriously threaten Washington DC or some of the other core Union states it MIGHT have brought the Union to the table for some sort of peace treaty that would allow the South to secede and have the Union accept that formally.
Did Davis forbid Lee to do, enter a Union state, take a particular city?
I’m going with this … and since we’re being creative … let’s have the victorious CSA go ahead and burn Washington DC to the ground, throw in a Philadelphia and New York City in embers … if the Army of the Potomac is destroyed, I would see a bright future for the CSA.
The CSA would likely have wanted Washington for its own capital, believing as it did that it was the true heir to the sainted Founding Fathers’ dream etc.
That would just piss the Union off, and as said much later “Awaken a Sleeping Giant and fill him with a terrible resolve.”
I will argue the Battle of Atlanta. Had Davis not replaced Joe Johnston with Hood then possibly McClellan wins the Election of 1864. It worries me that the OP picked the Battle of Vicksburg. I would have referred to it as the Siege of Vickburg and the battle was another issue. Secondly, let’s say Pemberton defeats Grant - then what? You could discuss Chancelorville, specifically what if Jackson survives and then is at Gettysburg.
OR the OP could have Davis actually organize the CSA army quickly after first Battle of Manassas, recognize the seniority of Johnston over Beauregard* and press down on Washington.
*For the OP, Johnston seniority was a major issue throughout the war.