Meshike was the final battle in the young Emperor Gordian's (Marcus Antonius Gordianus Pius) campaign against Sassanid Persia. He was only 19 at the time and had been on the throne for 6 years. Virtually nothing is known about the battle it is only mentioned by name in Persian sources where it is portrayed as a great Persian victory. It is glossed over or not mentioned by the Romans. What is known is that Gordian lost his life. he either fell from his horse in battle and later died of his injuries or he was murdered by his troops at the instigation of Philip the Arab (Marcus Julius Philippus). Either way Gordian died and Philip became Emperor, making peace with the Persians.
The initial campaign had gone well with the Romans winning several battles and recovering the cities of Nisibis and Carrhae. However Gordian's mentor (and father-in-law) Gaius Furius Sabinius Aquila Timesitheus, the Praetorian Prefect, was killed in an earlier battle (possibly at Resaena in Syria). He was been replaced by Philip who immediately began plotting against the Emperor. He deliberately starved the troops of supplies and trying to stir up mutiny.
Here is what some original sources say:
When I (Shapur I) was first established over the domination of the nations, the Caesar Gordian from the whole of the Roman Empire and the nations of the Goths and the Germans raised an army and marched against Assyria, against the nation of the Aryans and against us. A great battle took place between the two sides on the frontiers of Assyria at Meshike. Caesar Gordion was destroyed and the Roman Army was annihilated. (Inscription of Shapur)
The Emperor, having made all possible preparations, marched against the Persians. The Roman army appeared to have the upper hand in the first engagement but the death of Timesitheus, the Praetorian Prefect , considerably damaged the emperor's confidence...Philip was chosen praetorian prefect in his place and soon the good will of the troops towards the emperor abated. Once he assumed office he (Philip) began to aspire to imperial dignity and endeavoured to seduce all the soldiers who were disposed to revolt.(Zosimus)
(Gordian) left Italy for Persia and afterwards routed Shapur, the king of the Persians, in battle and brought Nisibis and Carrhae under subjugation... but as he was approaching Ctesiphon, he was murdered by his own troops at the instigation of the Prefect Philip.(Syncellus)
However other sources tell a different story
(Gordian) campaigned against the Persians and fell in with them. He drove his horse forward into battle, exhorting his men and stirring them to feats of courage. The horse stumbled and fell on him, crushing his thigh. He therefore returned to Roman and died from the fracture after a reign of 6 years.(Zonaras)