Hi there, late reply, but you might be thinking of the civil war between emperors Constantius and Julian in 360. Constantius was the Augustus, the senior emperor of the entire Roman Empire, but the Romans felt the imperial territory was too large for one person to manage, so Constantius appointed his cousin, Julian (one of Constantius' last living relatives, because he and his brothers has executed most others for being potential imperial rivals) as a junior emperor, known as a Caesar, in late 355.

This happened in the wake of a rebellion and civil war in the western Empire, and to help him be victorius in that war, Constantius had incited a siginificant number of Germanic barbarians to invade across the Rhine River. But once he had won the civil war, the invading barbarians now became Constantius' problem. So he placed himself in command of the Italian army, and Julian in command of the Gallic army, and they both co-ordinated to drive the barbarians back over the Rhine in 356. Constantius clearly felt the situation had stabilised, because in 357 he left and moved to the Danube theatre to oversee its defense, and then he would eventually move back to Antioch, near the border with the Persian Empire.

Julian remained in Gaul, and campaigned every year against barbarians, most often the Alemanni. However, perhaps because Constantius had orchestrated the death of so much of his family, and also because he continually appointed ministers and officials to oversee him and supress Julian's independence, the Caesar began plotting a rebellion of his own. He orchestrated the removal of at least one of his highest generals, and sidelined the others that were placed in command of his armies. This meant that when Julian was victories against the Alemanni, the credit and honour fell to him alone. This helped the western army develop a strong tie of loyalty to Julian, and in early 360 they proclaimed him to be a full Augustus, a rival of Constantius.

This was never going to be acceptable to Constantius, but he was busy stemming the attacks by the aggressive Persian king, Shapur II, who had invaded and sacked a major Roman city in 359. So the initiative was on Julian, who marched his forces eastwards and captured the important city of Sirmium. He halted, probably intending to spend the winter there, because Constantius had sent some of his army to occupy the roads and mountain passes Julian would need to continue moving east. Additionally, the city of Aquileia in northern Italy had turned against him, cutting him off from Italy and an easy resupply route from his powerbase in Gaul. Julian would have been facing the prospect that the following year he would have to deal with either a siege of Constantinople, or probably more likely, a pitched battle in the field with Constantius' army. It was a dire situation, and throughout the fourth century, the eastern army prevailed in civil war. Julian obviously did not have this hindsight like we do, so probably could not have known how unlikely he was to survive the battles of the following year. However, while en route to Constantinople, emperor Constantius died of illness in October or November (the accuracy of the manuscript of the ancient historian Ammianus Marcellinus, which says October, had been doubted and corrected to November).

Now onto the final and controversial part, whether Constantius proclaimed Julian as the rightful heir before he died. Ammianus Marcellinus is the best historian of this period. He was a medium-high ranking officer in Constantius' army around this time (it is unclear exactly when he retired, it may have been as early as 359, or as late as 364). In Book 21, Chapter 15, Lines 4-6, he describes what happened after Constantius died. He said that the ministers and officials in Constantius' court were the first to consider what should be done. They first considered that they might raise one of their own as an eastern emperor, presumably to continue the civil war, but they felt this was too risky. Proclaiming a new emperor had a high chance of fragmenting their own army amongst different factions, and with Julian so close, he could easily crush them while they were divided. In the end, they ordered some officials to go to Julian and deliver the news, and beg him to come to the east and take over control. Next, Ammianus does something he often does, which is write that 'rumours and uncertain reports' spread the tale that Constantius had a last will and testament that proclaimed Julian as an heir. Ammianus seems to have often done this when he wanted to record something he believed to be true, but did not have proof or evidence of. So he must not have seen Constantius' will or even spoken to someone he trusted that had seen it, but he still believed there was a high chance that it existed. Personally, it seems like too convienient for the officials who propagated the tale. They knew that there was a high chance Juliann would execute them for supporting his enemy, but if they could smoothly hand over the eastern Empire, there was a chance they might be spared.